President's Address. 
55 
tion. ^^Tay, I will go farther and say — if we fail here , we fail in the 
end to which the others are but means. What avails it that we 
have arsenals stored with the choicest weapons, if our arms be too 
indolent or too weak to wield them ? What avails it that we have a 
Library replete with books, which should aid us in investigating the 
truths of science or of criticism ; or a Museum rich in the materials 
by which the history of our country is to be written, if, through our 
inactivity, the mines of literature or science be unworked, at least 
by us, and our Museum fulfil no higher function than that of a collec- 
tion of pretty curiosities to amuse an idle hour ? I am far from say- 
ing that the labour expended on these collections is, even then, useless. 
But if you should be disposed to look on such a state of things with self- 
complacency, remember that, although we have done well in accumu- 
lating materials, which a stronger generation may use, it is not the 
less a reproach to us that ive have failed to use them. Do we merit 
that reproach now ? We must not shrink from the question. 
What answer can we give to that question in the department 
of Science ? Does our history for the last five years show progres- 
sive or even sustained activity ? I cannot say that the answer is 
satisfactory. The number of scientific communications made to the 
Academy during that period does show a diminution sufficiently 
marked to attract our most earnest attention. This diminution we 
must try to arrest ; and that we may do so effectually, let us, in the 
first place, seek to interpret it, by examining successively the several 
great divisions of science, and comparing the progress which they 
have made in our hands with their advance in the scientific world 
generally. 
And first, with regard to Pure Mathematics. Here the diminu- 
tion during the last five years is very marked indeed, even as com- 
pared with the preceding five years, and still more as compared with 
the ten years from 1850 to 1860. But it is necessary to observe that 
there are circumstances connected with Pure Mathematics which 
render a diminution of activity here less significant than it would 
be in other branches of science. In the first place, the progress 
of the science itself is not as rapid at present as it has been in 
other periods of scientific history. This slackening is particularly 
apparent in a branch of Pure Mathematics which was, at one time, a 
highly-favoured subject with Irish mathematicians — I mean the geo- 
metry of surfaces. The impulse given to this study by the disco- 
veries of Chasles appears to have much abated, and this abatement has 
probably operated largely in producing an effect which is greatly 
to be deplored — namely, that, with some honourable exceptions, the 
younger Irish mathematicians have not contributed to the Irish 
Mathematical School all that they might have given. But, passing 
by this consideration, I would remind you that we are not the only 
society which has to remark upon a diminution in the number of 
communications in Pure Mathematics. Compare, for example, the 
number of such communications read before the Eoyal Society during 
