culties to one who is by profession a pure mathematician, and 
who, in other branches ofscience, can only aspire to be regarded 
as an amateur. 
But, although I thus contess myself a specialist, and a 
: a it may be said of a narrow kind, I shall not venture, in 
t 
few remarks which I now propose to make, to indulge my 
own speciality too far. 
I am well aware that we are certain, in this section, to have a 
sufficient number of communications, which of necessity assume 
a special and even an abstruse character, and which, whatever 
pains may be taken to give them clearness, and however valuable 
may be the results to which they lead, are nevertheless ex- 
tremely difficult to follow, not only for a popular audience, 
but even for men of science whose attention has not been 
specially, and recently, directed to the subject under dis- 
cussion. I should think it, therefore, almost unfair to the 
section, if at the very commencement of its proceedings I 
were to attempt to direct its attention in any exclusive manner 
to the subject which, I confess, if I were left to myself, I should 
most naturally have chosen—the history of the advances that 
have been made during the last ten or twenty years in mathe- 
matical science, Instead, therefore, of adventuring myself on 
this difficult course, which, however, I strongly recommend to 
some successor of mine less scrupulous than myself, I propose, 
though at the risk of repeating what has been better said by 
others before me, to offer some general considerations which may 
have a more equal interest for all those who take part in the 
proceedings of this section, and which appear to me at the 
present time to be more than usually deserving of the notice of 
those who desire to promote the growth of the scientific spirit in 
this country. I intend, therefore, while confining myself as 
strictly as I can to the range of subjects belonging to this section, 
to point out o1e or two, among many, of the ways in which 
sectional meetings, such as ours, may contribute to the advance- 
ment of science. A 
We all know that Section A of the British Association is the 
section of mathematics and physics ; and I dare say that many 
of us have often thought how astonishingly vast is the range of 
subjects which we slur over, rather than sum up, in this brief 
designation. We include the most abstract speculations of pure 
mathematics, and we come down to the most concrete of all phe- 
nomena—the most every-day of allexperiences. I think I have 
heard in this section a discussion on spaces of five dimensions, 
and we know that one of our committees, a committee which is of 
long-standing, and which has done much useful work, reports 
to us annually on the Rainfall of the British Isles, Thus our wide 
range coversthe mathematics of number and quantity in their most 
abstract forms, the mathematics of space, of time, of matter, of 
motion, and of force, the many sciences which we comprehend 
under the name of astronomy, the theories of sound, of light, 
heat, electricity ; and besides the whole physics of our earth, sea, 
and atmosphere, the theory of earthquakes, the theory of tides, 
the theory of all the movements of the air, from the lightest rip- 
ple that affects the barometer up toacyclone. As I have already 
said, it is impossible that communications on all these subjects 
should be interesting, or indeed intelligible, to all our members ; 
and, notwithstanding the pains taken by the committee and by the 
secretaries to classify the communications offered tous, and to place 
upon the same days those of which the subjects are cognate to 
one another, we cannot doubt that the disparateness of the ma- 
terial which comes before us in this section is a source of serious 
inconvenience to many members of the Association. Occa- 
sionally, too, the pressure upon our time is very great, and we are 
obliged to hurry over the discussions on communications of great 
importance, the number of papers submitted to us being, of 
course, in a direct proportion to the number of the subjects in- 
cluded in our programme. It has again and again been proposed 
to remedy these admitted evils by dividing the section, or at 
least by resolving it into one or more sub-sections. But I con- 
fess that I am one of those who have never regretted that this 
proposal has not commended itself to the Association, or indeed 
to the section itself. I have always felt that by so sub-dividing 
ourselves we should run the risk of losing one or two great ad- 
vantages which we at present possess ; and I will briefly state 
what, in my judgment, these advantages are, 
I do not wish to undervalue the use to a scientific man of 
listening to and taking part in discussions on subjects which lie 
wholly in the direction in which his own mind has been working. 
But 1 think, nevertheless, that most men who have attended a 
meeting of this Association, if asked what they have chiefly 
gained by it, would answer in the first place that they have had 
NATURE 
449 
opportunities of forming or of renewing those acquaintances or 
intimacies with other scientific men which, to most men engaged 
in scientific pursuits, are an indispensable condition of successful 
work ; and in the second place, that while they may have heard but 
little relating to their own immediate line of inquiry which they 
might not as easily have found in Journals or Transactions else- 
where, they have learned much which might otherwise have 
never come to their knowledge of what is going on in other di- 
rections of scientific inquiry, and that they have carried away 
many new conceptions, many fruitful germs of thought, caught 
perhaps from a discussion turning upon questions apparently very 
remote from their own pursuits. An object just perceptible on 
a distant horizon is sometimes better descried by a careless side- 
ward glance than by straining the sight directly at it; and so 
capricious a gift is the inventive faculty of the human mind that 
the clue to the mystery hid beneath some complicated system of 
facts will sometimes elude the most patient and systematically 
conducted search, and yet will {reveal itself all of a sudden upon 
some casual suggestion arising in connection with an apparently 
remote subject. I believe that the mixed character and wide 
range of our discussions has been most favourable to such happy 
accidents. But even apart from these, if the fusion in this sec- 
tion of so many various branches of human knowledge tends in 
some degree to keep before our minds the essential oneness of 
science, it does us a good service, There can be no question 
that the increasing specialisation of the sciences, which appears 
to be inevitable at the present time, does nevertheless constitute 
one great source of danger for the future progress of human 
knowledge. This specialisation is inevitable, because the further 
the boundaries of knowledge are extended in any direction, the 
more laborious and time-absorbing a process does it become to 
travel to the frontier ; and thus the mind has neither time nor 
energy to spare for the purpose of acquainting itself with regions 
that lie far away from the track over which it is forced to travel. 
And yet the disadvantages of excessive specialisation are no less 
evident, because in natural philosophy, as indeed in all things 
on which the mind of man can be employed, a certain wideness 
of view is essential to the achievement of any great result, or to 
the discovery of anything really new. The twofold caution so © 
often given by Lord Bacon against over-generalisation on the 
one hand, and against over-specialisation on the other, is still as 
deserving as ever of the attention of mankind. But in 
our time, when vague generalities and empty metaphysics 
have been beaten once, and we may hope for ever, 
out of the domain of exact science, there can be but 
little doubt on which side the danger of the natural philoso- 
pher at present lies. And perhaps in our section, as at present 
constituted, there is a freer and fresher air—we are, perhaps, a 
less inadequate representation of ‘‘that greater and common 
world ” of which Lord Bacon speaks, than if we were subdivided 
into as many parts as we include—I will not say sciences—but 
groups of sciences. Perhaps there is something in the very 
diversity and multiplicity of the subjects which come before us 
which may serve to remind us of the complexity of the problems 
of science, of the diversity and multiplicity of nature. 
On the other hand it is not, as it seems to me, difficult to 
assign the nature of the unity which underlies the diversity of 
our subjects, and which justifies, to a very great extent, the juxta- 
position of them in our section. That unity consists not so 
much in the nature of the subjects themselves, as in the nature 
of the methods by which they are treated. A mathematician, at 
least—and it is asa mathematician I have the privilege of address- 
ing you—may be excused for contending that the bond of union 
among the physical sciences is the mathematical spirit and the 
mathematical method which pervades them. As has been said 
with profound truth by one of my predecessors in this chair, our 
knowledge of nature, as it advances, continuously resolves differ- 
ences of quality into differences of quantity. All exact reasoning 
—indeed all reasoning—about quantity is mathematical reason- 
ing; and thus as our knowledge increases, that portion of it 
which becomes mathematical increases at a still more rapid rate, 
Of all the great subjects which belong to the province of this 
section, take that which at first sight is the least within the 
domain of mathematics—I mean meteorology. Yet the part 
which mathematics bears in meteorology increases every year, 
and seems destined to increase. Not only is the theory of the 
simplest instruments of meteorology essentially mathematical, 
but the discussion of the observations—upon which, be it remem. 
bered, depend the hopes which are already entertained with 
increasing confidence, of reducing the most variable and com- 
plex of all known phenomena to exact laws—is a problem which 
