NOTICES AND ABSTRACTS 



OP 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 



Address hy J. Clekk Maxweli,, LL.D., F.R.S., President of the Section. 



At several of the recent Meetings of the British Association the varied and im- 

 portant 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 aiTay of symbols and 

 brackets which form the armouiy of the mathematician, or the dry results whicli 

 are only the monuments of his conquests, but the mathematician himself, with all 

 his human faculties directed by his professional sagacity to the pursuit, apprehen- 

 sion, 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 symmetry formed by the combination of his own sub- 

 ject with those of the foi-mer 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. Tj-ndall'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 natm-e of Mathematical 

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

 others in contact) to build up the Ideal Pyramid is a discourse on the Relation of 

 the two branches (Mathematics and Physics) to, their action and reaction upon, 

 one another, a magnificent theme, with which it is to be hoped that some future 

 President of Section A will crown the edifice and make the Tetralogy (symbolizable 

 by A+A', A, A', A A') complete." 



The theme thus distinctly laid down for his successor by our late President is 

 indeed a magnificent one, far too magnificent for any efforts of mine to realize. I 

 have endeavoured to follow Mr. Spottiswoode, as with far-reaching vision he dis- 

 tinguishes the systems of science into which phenomena, om* Imowledge of which 

 is still in the nebulous stage, are growing. I have been carried by the penetrating 

 insight and forcible expression of Dr. Tyndall into that sanctuary of minuteness and 

 of power where molecules obey the laws of their existence, clash together in fierce 

 1870. 1 



/ 



