NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
Address by The Rey. Professor J. H. Jetuerr, W.A., M.R.I.A., President of 
the Section. 
In opening the business of the Section, my first duty is, as you will naturally 
anticipate, to return my warmest thanks to the British Association for the honour 
which they have conferred upon me by inviting me to occupy this Chair. I do it, 
T assure you, with all sincerity, fully sensible how high the compliment is; and if 
I do not dwell further upon the subject, it is, as I hope you will believe, because 
the President of a Section ought to occupy your time, not by speaking of himself 
or his own feelings, but by a review, more or less extensive, of those branches of 
science which form the proper business of the Section. 
I say “ more or less extensive ;” for in determining what kind of review he will 
present to you, the President of this Section has a very wide range of choice. 
He may give you a rapid but (in its outline) complete sketch of the progress of 
mathematical science during the past year. He may select some one special sub- 
ject, probably (and rightly) the ro ee with which he is himself especially con- 
versant, giving of that a more detailed account; or he may take a middle course, 
neither so extensive as the first nor quite so limited asthe second. It is this latter 
course which I wish now to take, proposing to direct your attention, during the short 
time which I can allow myself, to the relations, becoming every day more fully de- 
veloped, not only among the branches of science which properly belong to us, but 
between our Section and the other Sections of the Association, or, in other words, 
between the sciences which we ordinarily call mathematical or physical and some 
of the other sciences to which the British Association is devoted. I am the more 
anxious to direct your attention to this class of subjects, because recent investigation 
has shown how fertile for discovery the “ border land,” if I may so call it, between 
sciences hitherto considered distinct has been found to be. Instances in proof of 
this will present themselves as we go on; some have no doubt suggested themselves 
to you already. 1 
We are called, in ordinary language, the Mathematical Section. The adjective 
must indeed be understood in a very wide sense—too wide perhaps for strict pro- 
riety of language, if it be meant to include every thing to which our labours 
eve are devoted ; still the use of the term “mathematical ” indicates, and truly 
indicates, the preponderance which in this Section we give to mathematics and 
to those sciences which are at present capable of mathematical treatment; and 
therefore the first question which in the consideration of our present subject 
naturally presents itself is, Does this list of sciences show any prospect of increase ? 
Are we making, are we likely to make, an increased use of mathematics as an 
instrument of physical investigation? Are we trying to improve its use in those 
E 
1874. 
