NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
MatTHEMATICS. 
Address by G. G. Stoxns, M.A., F.RS. Sc., Lucasian Professor of 
Mathematics in the University of Cambridge. 
{r has been customary for some years, in opening the business of the Section, for 
the President to say a few words respecting the object of our meetings. In this Sec- 
tion, more perhaps than in any other, we have frequently to deal with subjects of 
a very abstract character, which in many cases can be mastered only by patient 
study, at leisure, of what has been written. The question may not unnaturally be 
asked—If investigations of this kind can best be followed by quiet study in one’s 
own room, what is the use of bringing them forward in a sectional meeting at all? 
I believe that good may be done by public mention, in a meeting like the present, 
of even somewhat abstract investigations; but whether good is thus done, or the 
audience are merely wearied to no purpose, depends upon the judiciousness of the 
person by whom the investigation is brought forward. It must be remembered that 
minute details cannot be Slowed in an exposition vird voce; they must be studied 
at leisure ; and the aim of an author should be to present the broad leading ideas 
of his research, and the principal conclusions at which he has arrived, clearly and 
briefly before the Section. It is then possible to discuss the subject-matter; to 
offer suggestions of new lines of experiment, or new combinations of ideas; and 
such discussions and suggestions, it seems to me, are among the most import-— 
ant business of a meeting such as this, Any one who has worked in concert 
with another zealously engaged in the same research must have felt the benefit 
arising from the mutual interchange of ideas between two different minds. Sug- 
gestions struck out by one call up new trains of thought and fructify in the mind 
of another; whereas they might haye remained barren and unfruitful in the mind 
of the original suggester. The benefit of cooperation is by no means confined to 
the one bed out, according to a preconcerted plan, of a research involving labour 
rather than invention; it is felt in a most delightful form in the procecution of 
original investigations. In a meeting like the present, we have the benefit of the 
mutual suggestions, not of two, but of many persons, whose minds are directed to 
the same object. The number of papers already in the hands of your Secretaries 
shows that there will be no lack of matter in this Section: the difficulty will rather, 
I apprehend, be to get through the business before us in the time prescribed. On 
this account the Section will, I hope, bear with me if I should sometimes feel my- 
self compelled, in justice to the authors of papers which are placed later on our 
lists, to cut short reusetons which otherwise might have been further prolonged 
with some interest. 
1862. 1: 
