and that we should strive to make them worthy of this rapidly 

 increasing town. Why should not our meetings be as attrac- 

 tive, and as interesting ; our transactions as important, and 

 as instructive, as those of similar Societies in other cities? 

 Influenced by this feeling, I have preferred to bring before 

 you, rather than any humbler researches of my own, the deep 

 and subtle speculations of one who stands in the very highest 

 rank among the mathematicians of Europe ; who, by a rare 

 combination of those diversities of genius — once found in 

 Plato, that first of human intelligences — unites the imagina- 

 tion and the fancy of the poet, with the abstractions of the 

 geometer. You already anticipate me, when I pronounce the 

 name of Sir W. Hamilton. 



"That we should assemble together for the advancement 

 of that which it is our avowed object to promote, is, I am 

 convinced, most desirable ; and the utility of those meetings 

 has been, in these latter times, fully appreciated, acknow- 

 ledged, and acted upon, not only in this country, but all 

 over Europe ; as witness the annual proceedings of the 

 British Association, and the various reunions, the literary 

 congresses of learned men, upon the Continent. And here 

 I may be pardoned a very slight digression, if I allude, in 

 passing, to one or two popular objections which have been 

 made against those associations, or congresses of men who 

 take an interest in the promotion of literature and the 

 advancement of science. The reason why I refer to the sub- 

 ject is this ; that if the objections, thus plausibly advanced, 

 are founded in truth, they hold equally well against our 

 meeting here this evening, as they do against the assembling 

 of men together, some of them from the remotest quarters of 

 Europe and America, at the annual congresses of the British 

 Association. 



" It has been said, What is the use of those meetings ? Can 

 we point to any great discovery that has been made at Oxford, 

 or at Cambridge, or at Dublin, or at York, or at any other 



