[From the British Association Report, Vol. XL.] 



XLI. Address to the Mathematical and Physical Sections of the British 



Association. 



[Liverpool, September 15, 1870.] 



AT several of the recent Meetings of the British Association the varied 

 and important business of the Mathematical and Physical Section has been 

 introduced by an Address, the subject of which has been left to the selection 

 of the President for the time being. The perplexing duty of choosing a subject 

 has not, however, fallen to me. 



Professor Sylvester, the President of Section A at the Exeter Meeting, 

 gave us a noble vindication of pure mathematics by laying bare, as it were, 

 the very working of the mathematical mind, and setting before us, not the 

 array of symbols and brackets which form the armoury of the mathematician, 

 or the dry results which are only the monuments of his conquests, but the 

 mathematician himself, with all his human faculties directed by his professional 

 sagacity to the pursuit, apprehension, and exhibition of that ideal harmony 

 which he feels to be the root of all knowledge, the fountain of all pleasure, 

 and the condition of all action. The mathematician has, above all things, an 

 eye for symmetry ; and Professor Sylvester has not only recognized the sym- 

 metry formed by the combination of his own subject with those of the former 

 Presidents, but has pointed out the duties of his successor in the following 

 characteristic note : 



" Mr Spottiswoode favoured the Section, in his opening Address, with a com- 

 bined history of the progress of Mathematics and Physics ; Dr. Tyndall's address 

 was virtually on the limits of Physical Philosophy ; the one here in print," says 

 Prof. Sylvester, "is an attempted faint adumbration of the nature of Mathe- 

 matical Science in the abstract. What is wanting (like a fourth sphere resting 



