| Sept. 22, 1870] 
NATURE 
419 
of the Council, they must be sent to the assistant general secre- 
tary at least one month before the meeting of the Association. 
The decision of the Council on the claims of any member of the 
Association to be placed on the list of the General Committee to 
be final. 
CLASS B.—TEMPORARY MEMBERS 
3. The president for the time being, or, in his absence, one 
delegate representing him, of any scientific society publishing 
transactions, Claims under this rule to be sent to the assistant 
general secretary before the opening of the meeting. 
4. Office-bearers for the time being, or delegates, altogether 
not exceeding three, from scientific institutions established in the 
place of meeting. Claims under this rule to be approved by the 
local secretaries before the opening of the meeting. 
5. Foreigners and other individuals whose assistance is de- 
sired, and who are specially nominated in writing, for the meeting 
of the year, by the president and general secretaries, 
6. Vice-presidents and secretaries of sections.” 
SECTIONAL PROCEEDINGS 
Section A.—Mathematical and Physical Science.—President, 
Prof. J. Clerk Maxwell, F.R.S. 
The president delivered the following address :— 
Art several of the recent meetings of the British Association 
the varied and important business of the Mathematical and 
Physical Section has been introduced by an Address, the 
subject of which has been left to the selection of the president 
for the time being. The perplexing duty of choosing a subject 
has not, however, fallen to me. Professor Sylvester, the presi- 
dent of Section A at the Exeter meeting, gave us a noble 
vindication of pure mathematics by laying bare, as it were, the 
very working of the mathematical mind, and setting before us, 
not the array of symbols and brackets which form the armoury 
of the mathematician, or the dry results which are only the 
monuments of his conquests, but the mathematician himself, 
with all his human faculties directed by his professional sagacity 
to the pursuit, apprehension, and exhibition of that ideal har- 
mony which he feels to be the root of all knowledge, the fountain 
of all pleasure, and. the condition of allaction. The mathema- 
tician has, above all things, an eye for symmetry ; and Professor 
Sylvester has not only recognised the symmetry formed by the 
combination of his own subject with those of the former presi- 
dents, but has pointed out the duties of his successor in the 
following characteristic note -— 
‘Mr. Spottiswoode favoured the Section, in his opening 
address, with a combined history of the progress of mathematics 
and physics ; Dr. Tyndall’s address was virtually on the limits 
of physical philosophy ; the one here in print,” says Professor 
Sylvester, ‘fis an attempted faint adumbration of the nature of 
mathematical science in the abstract. What is wanting (like a 
fourth sphere resting on three others in contact) to build up the 
ideal pyramid is a discourse on the relation of the two branches 
(mathematies and physics) to, and their action and reaction upon, 
one another—a magnificent theme, with which it is to be hoped 
that some future president of Section A will crown the edifice, 
and make the tetralogy (symbolisable by A+ A’, A, A’, AA’) 
complete.” 
The theme thus distinctly laid down for his successor by our 
Jate President is indeed a magnificent one, far too magnificent for 
any efforts of mine to realise. I have endeavoured to follow Mr. 
Spottiswoode, as with far-reaching vision he distinguishes the 
systems of science into which phenomena, our knowledge of 
which is still in the nebulous stage, are growing. I have been 
carried by the penetrating insight and forcible expression of Dr. 
Tyndall into that sanctuary of minuteness and of power where 
molecules obey the laws of their existence, clash together in 
fierce collision, or grapple in yet more fierce embrace, building 
up in secret the forms of visible things. I have been guided by 
Professor Sylvester towards those serene heights 
“© Where never creeps a cloud, or moves a wind, 
Nor ever falls the least white star of snow, 
Nor ever lowest roll of thunder moans, 
Nor sound of human sorrow mounts, to mar 
Their sacred everlasting calm,” 
But who will lead me into that still more hidden and dimmer 
region where Thought weds Fact ; where the mental operation of 
the mathematician and the physical action of the molecules are 
seen in their true relation? Does not the way to it pass through 
the very den of the metaphysician, strewed with the remains of 
former explorers, and abhorred by every man of science? It 
would indeed be a foolhardy adventure for me to take up the 
valuable time of the section by leading you into those speculations 
which require, as we know, thousands of years even to shape 
themselves intelligibly. 
But we are met as cultivators of mathematics and physics. 
In our daily work we are led up to questions the same in kind 
with those of metaphysics ; and we approach them, not trustiny 
to the native penetrating power of our own minds, but trained 
by a long-continued adjustment of our modes of thought to the 
facts of external nature. As mathematicians, we perform certain 
mental operations on the symbols of number or of quantity, and, 
by proceeding step by step from more simple to more complex 
operations, we are enabled to express the same thing in many 
different forms. The equivalence of these different forms, though 
a necessary consequence of self-evident axioms, is not always, to 
our minds, self-evident ; but the mathematician, who, by long 
practice, has acquired a familiarity with many of these forms, 
and has become expert in the processes which lead from one to 
another, can often transform a perplexing expression into another 
which explains its meaning in more intelligible language. 
As students of physics, we observe }henomena under varied 
circumstances, and endeavour to deduce the laws of their rela- 
tions. Every natural phenomenon is, to our minds, the result of 
an infinitely complex system of conditions. What we set our- 
selvesto do is to unravel these conditions, and by viewing the phe- 
nomenon in a way which is in itself partial and imperfect, to piece 
out its features one by one, beginning with that which strikes us 
first, and thus gradually learning how to look at the whole 
phenomenon so as to obtain a continually greater degree of clear- 
ness and distinctness. In this process, the feature which presents 
itself most forcibly to the untrained inquirer may not be that 
which is considered most fundamental by the experienced man of 
science ; for the success of any physical investigation depends on 
the judicious selection of what is to be observed as of primary 
importance, combined with a voluntary abstraction of the mind 
from those features which, however attractive they appear, we 
are not yet sufficiently advanced in science to investigate with 
pre fit. 
Intellectual processes of this kind have been going on since 
the first formation of language, and are going on still. Nodoubt 
the feature which strikes us first and most forcibly in any pheno- 
menon, is the pleasure or the pain which accompanies it, and the 
agreeable or disagreeable results which follow after it, A theory 
of nature from this point of view is embodied in many of our 
words and phrases, and is by no means extinct even in our deli- 
berate opinions. It wasa great step in science when men be- 
came convinced that, in order to understand the nature of things, 
they must begin by asking, not whether a thing is good or bad, 
noxious or beneficial, but of what kind is it? and how much is 
there of it? Quality and quantity were then first recognised as 
the primary features to be observed in scientific inquiry. As 
science has been developed, the domain of quantity has every- 
where encroached on that of quality, till the process of scientific 
inquiry seems to have become simply the measurement and 
registration of quantities, combined with a mathematical dis- 
cussion of the numbers thus obtained. It is this scientific method 
of directing our attention to those features of phenomena which 
may be regarded as quantities which brings physical research 
under the influence of mathematical reasoning. In the work of 
the section we shall have abundant examples of the successful 
application of this method to the most recent conquests of science ; 
but I wish at present to direct your attention to some of the 
reciprocal effects of the progress of science on those elementary 
conceptions which are sometimes thought to be beyond the reach 
of change. 
If the skill of the mathematician has enabled the experi- 
mentalist to see that the quantities which he has measured are 
connected by necessary relations, the discoveries of physics have 
revealed to the mathematician new forms of quantities which he 
could never have imagined for himself. Of the methods by 
which the mathematician may make his labours most useful 
to the student of nature, that which I think is at present 
most important is the systematic classification of quantities. 
The quantities which we study in mathematics and phy- 
sics may be classified in two different ways. The student 
who wishes to master any particular science must make himself 
familiar with the various kinds of quantities which belong to that 
science. When he understands all the relations between these 
quantities, he regards them as forming a connected system, and 
he classes the whole system of quantities together as belonging 
