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TRANSACTIONS OF THE SECTIONS, 
Suction AA—MATHEMATICAL AND PHYSICAL SCIENCE. 
PRESIDENT OF THE SECTION—J. W. L. GLAISHER, S¢c.D., F.R.S , V.P.R.A.S. 
THURSDAY, SEPTEMBER 4. 
The PresrpEnT delivered the following Address :— 
No one who is called upon to preside over this section can fail to be struck by 
the range of subjects comprehended within its scope. The field assigned to us 
extends from the most exact of all knowledge, the sciences of number, quantity, 
and position, to branches of inquiry in which the progress has been so slight that 
they still consist of little more than collections of observed facts. This breadth of 
area has obvious disadvantages, but it is not without some compensating advan- 
tages. In these days when science is so much subdivided it is well that. students 
of subjects even so diverse as those with which we have tu deal should occasionally 
meet on common ground, and have the opportunity of learning from each other’s 
lips the kind of work in which they are engaged. Wide as is our range, we 
should remember also how closely knit together in various ways are the more 
important of our subjects; and in the case of Mathematics, Astronomy, and 
Physics, besides their actual and historical alliance, a mathematician may be 
permitted to feel that a special bond of union is created by the mathematical 
processes and language which are essential for their investigation and expression. 
It is, I am afraid, unfortunate for my audience, that my own subject should be 
at one extreme, not only of those dealt with by our section, but even of the still 
greater range covered by the Association, I will endeavour, however, in my 
remarks to confine myself to a few general considerations relating to pure mathe- 
matics which I hope will not be considered out of place on this occasion. 
By pure mathematics I do not mean the ordinary processes of algebra, 
differential and integral calculus, &c., which every worker in the so-called 
mathematical sciences should have at his command. I refer to the abstract 
_ sciences which do not rest upon experiment in the ordinary sense of the term, their 
fundamental principles being derived from observations so simple as to be more or 
less axiomatic. To this class belong the theories of magnitude and position, the 
former including all that relates to quantity, whether discrete or continuous, and 
the latter including all branches of geometry. The science of continuous magni- 
tude is alone a vast region, containing many beautiful and extensive mathematical 
theories. Among the more important of these may be mentioned the theories 
of double and of multiple periodicity, the treatment of functions of complex 
variables, the transformation of algebraical expressions (modern algebra), and the 
higher treatment of algebraical and differential equations as distinguished from 
their mere solution. It is this kind of scientific exploration which fascinates 
