NOTICES AND ABSTRACTS 



OF 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 



Address by Prof. H. J. S. Smith, M.A., F.B.S., President of tlie Section, 



For several years past it has been the custom for the President of this Section, as 

 of the other Sections of the Association, to open its proceedings with a brief address. 

 I am not willing upon this occasion to deviate from the precedent set by my 

 predecessors, although I feel that the task presents peculiar difficulties to one who 

 IS by profession a pure mathematician, and who in other branches of science can 

 only aspire to be regarded as an amateur. 



But although I thus confess myself a specialist, and a specialist it may be said 

 of a narrow kind, I shall not venture, in the few remarks which I now propose to 

 make, to indulge my own specialty too far. 



I am well aware that we are certain in this Section to have a sufficient number 

 of communications which of necessity assume a special and even an abstruse 

 character, and which, whatever paius may be taken to give them clearness, and 

 however valuable may be the results to which they lead, are nevertheless extremely 

 difficult to follow, not only for a popular audience, but even for men of science 

 whose attention has not been specially and recently directed to the subject under 

 discussion. I should think it, therefore, almost unfair to the Section if, at the very 

 commencement of its proceedings, I were to attempt to direct its attention in any 

 exclusive manner to the subject which I confess, if I were left to myself, I should 

 most naturally have chosen — the history of the advances that have been made 

 during the last ten or twenty years in mathematical science. Instead, therefore, 

 of adventuring myself on this difficult course, which, however, I strongly recom- 

 mend to some successor of mine less scrupulous than myself, I propose, though at 

 the risk of repeating what has been better said by others before me, to offer some 

 general considerations which may have a more equal interest for all those who take 

 part in the proceedings of this Section, and which appear to me at the present time 

 to be more than usually deserving of the notice of those who desire to promote 

 the growth of the scientific spirit in this country. I intend therefore, while 

 confining myself as strictly as I can to the range of subjects belonging to this 

 Section, to point out out one or two, among many, of the ways in which sectional 

 meetings such as ours may contribute to the advancement of Science. 



We all know that Section A of the British Association is the Section of Mathe- 

 matics and Physics ; and I dare say that many of us have often thought how 

 astonishingly vast is the range of subjects which we slur over, rather than sum up, 

 in this brief designation. We include the most abstract speculations of pure 

 mathematics, and we come down to the most concrete of all phenomena, the 

 most every-day of all experiences. I think I have heard in this Section a discussion 

 on spaces of five dimensions; and we know that one of our Committees, a Committee 

 1873. 1 



