NOTICES AND ABSTRACTS 



OF 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 



Mathematics. 

 Address by the Rev. Prof. Price, M.A., F.R.S., President of the Section. 



Gentlemen,— A custom has prevailed at our Meetings for some years for the Pre- 

 sident of each Section to make a short address at the opening. The object of it I 

 take to be twofold; first, to explain to new members the nature of the business which 

 we have to transact; and, secondly, to suggest to all the course of procedure, and 

 the distribution of subject most convenient for the conduct of our business. The 

 area of scientific research which this Section covers is very large, larger perhaps 

 than that of any other; and its subjects vary so much, that while to some of 

 those who frequent this room certain papers may appear dull, yet to others thev 

 will be full of interest. There are many and very good reasons why these subjects 

 should be grouped. Some of them possess, probably in the highest degree attain- 

 able by the human intellect, the characteristics of perfect and necessary science ; 

 while others are at present little more than a conglomeration of observations, made 

 indeed with infinite skill and perseverance, and of the greatest value ; capable 

 probably in time of greater perfection, nay, perhaps, of most perfect forms, but as 

 vet in their infancy, scarcely indicating the process by which that maturity will 

 be arrived at, and containing hardly the barest outline of their ultimate laws" We 

 have indeed sciences intermediate to these two extremes, in which some of the laws 

 are already capable of mathematical expression, and from which residts have been 

 derived, and still many phenomena are as yet not brought within their comprehen- 

 sion. But as all subjects which we regard in this Section are of one type, so are 

 they rightly combined; and it will be, I venture to think, an evil day for natural 

 knowledge, when we cease to regard the forms of the sciences of space, number, 

 and^ motion, as those to which all others ought to assimilate themselves. 



Now first of all in our Section stand Mathematics, both pure and applied. These, 

 indeed, require very heavy and arduous study, inasmuch as thev have peculiar 

 nomenclature, language, and processes, and thus it is only to the few generally who 

 have made them their particular study that they oiler great interest. Mathematics 

 have also now become so large in their grasp and so curious in their details, that I 

 am, 1 am sure, only expressing the opinions of most analysts when I say that the 

 whole of a man's life is not sufficient for more than one branch of it. Indeed 

 and we are proud to say so, some members of this Association are devotino- whole' 

 lives, and intellects too of the highest order, to the advancement of our knowledge 

 in a particular direction. Take, for instance, the theory of homogeneous forms : 

 in the history of science the names of Boole, Cavlev, * Sylvester will always be 

 recorded, and in scientific treatises their labours will find a place. Or take again 

 the theory of elliptic functions, or the calculus of probabilities ; the difficulties of 

 these subjects require the utmost tension of the human mind, and even then thev 

 transcend its limits. To many of the usual attendants on this Section, these and 

 kindred subjects may be dry and uninteresting. Well, if they are so to any of you 

 i must beg you to bear with us for a short time; these things have a deep "and 

 1860. i 



