TRANSACTIONS OF SECTION A. 549 



many of the keenest intellects among meu, and has grown to be one of the most 

 beautiful and wonderful theories among the many in the wide range of pure 

 mathematics ; or without entering upon the question whether geometry is a 

 pure or an applied science, I might review its growth alike in its projective, 

 its descriptive, its analytical, and its numerative divisions ; or I might trace the 

 influence of the idea of contiuuity in binding together subjects so diverse as 

 arithmetic, geometry, and functionality. What has been said already may, 

 however, suthce to 'give some slight indication of the vast and ever-widening 

 extent of pure mathematics. No less than in any other science knowledge gathers 

 force as it grows, and each new step once attained becomes the starting-point for 

 steady advance in further exploration. Mathematics is one of the oldest of the 

 sciences; it is also one of the most active, for its strength is the vigour of perpetual 

 youth. 



In conclusion, a few words are due to the personal losses caused since 

 eur last meeting. It is but little more than two years since Cayley passed 

 away; his life had been full of work, unhasting and unresting in the almost 

 placid course of his great mental strength. While Cayley was yet alive, one name 

 nsed to be coupled with his when reference was made to English pure 

 mathematics; the two great men were regarded as England's not unworthy 

 contribution to the exploration of the most abstract of the sciences. These fellow- 

 workers, diverse in temperament, in genius, in method, were bound by a friendship 

 that was ended only by death. And now Sylvester too has gone ; full of years 

 and honours ; though he lived long, he lived young, and he was happily active 

 until practically the very end. Overtlowing with an exuberant vitality alike 

 in thought and work, he preserved through life the somewhat rare laculty of 

 instilling his enthusiasm into others. Among his many great qualities, not 

 the least forcible were his vivid imagination, his eager spirit, and his abundant 

 eloquence. When he spoke and wrote of his investigations, or of the subject to 

 which the greater part of his thinking life had been devoted, he did it with the 

 fascination of conviction ; and at times— for instance, in his presidential address to 

 this Section at Exeter in 1869 — he became so possessed with his sense of the high 

 mission of mathematics, that his utterances had the lofty note of the prophet and 

 the seer. 



One other name must be singled out as claiming the passing tribute of our 

 homage ; for, in February last, the illustrious and venerable Weierstrass died. 

 He was unconnected with our Association ; but science is wider than our body, 

 and we can recognise and salute a master of marvellous influence and unchallenged 

 eminence. 



Thus, even to mention no others, pure mathematics has in a brief period lost 

 three of the very greatest of its pioneers and constructors who have ever lived. 

 We know their genius ; and the world of thought, though poorer by their loss, is 

 richer by their work. 



Tho' much is taken, much abides, and tho' 



We are not now that strength which in old days 



Moved earth and heaven ; that which we are, we are : 



One equal temper of heroic hearts, 



Made weak by lime and fate, but strong in will 



To strive, to seek, to find, and not lo jield. 



Knowledge cannot halt though her heroes fall : the example of their life-long 

 devotion to her progress, and the memory of their achievements, can inspire us 

 and, if need be, can stimulate us in realising the purpose for which we are banded 

 together as an Association — the advancement of science. 



The following Reports and Papers were read : — 



1. Report on Seismological Investigations 

 See Reports, p. 129. 



