58 
Proceedings of the Royal Irkh Aeadfuiy. 
soil from remaining barren. The most fertile, because the truest, 
inspiration Tvhich can fill the mind of the mathematical physicist 
comes fi'om the facts which experiment has collected. And here I 
would remind you that the benefit is fully reciprocated. Each can do 
for the other that which he cannot successfully do for himself. If the 
experimentalist recals the mathematician from the world of abstraction 
to the world of reality, the mathematician in turn can give to the 
observations of the experimentalist a coherence and a significance 
which he himself might have been unable to perceive. Analogies which 
he might never have observed — generalizations to which he might 
never have attained — may become at once apparent to that power of 
theoretic combination which his habits of thought have given to the 
mathematical physicist. 
The practical conclusion with regard to our studies here, and the 
mode of pursuing them, is not far to seek ; but as it is a conclusion 
applicable to eveiy part of our programme, and not only to those 
which we have been considering, I shall defer anything which I 
have to say on this branch of my subj ect till I have completed the 
survey of our progress in other parts of the field of Science. 
But, in passing from the subject of Applied Mathematics, I would 
express my earnest hope, that in the Irish Scientific School, the 
study of this great branch of Science may never be allowed to languish. 
It is here that the scientific historian has to record the noblest efforts 
of scientific genius. It is this which has given to us the " Principia," 
the '^Mecanique Analytique," the ^^Mecanique Celeste," works of 
which we may almost say that they are immortal as Science herself. 
And if we may be allowed to turn our gaze forward — if we may seek 
to penetrate the darkness which hangs over a region so vast as the 
future of Science — we may say that in Applied Mathematics we look on 
the future monarch of the scientific world. That day is indeed far dis- 
tant, and any attempt to precipitate its coming can but postpone it. Yet 
who can fail to see that the relation of Applied Mathematics to the 
domain of Science is one of unvarying conquest. Astronomy and 
Mechanics have long since yielded. Heat, Light, Sound, Electricity, 
Magnetism, are all but subdued ; and if Chemistry, with her vast and 
varied phenomena, still holds out, there are not wanting symptoms 
which allow us to hope that for her too the day will come, when, she 
shall fully vindicate her claim to the title of an exact science, by 
acknowledging the same authority. 
The contemplation of that vast though shadowy prospect, has in 
it a power which some would deny to Science. It can attract the 
imagination no less than the reason. Yet if we would show that the 
science which we have been considering does indeed possess that 
power, we need not look to the future. The records of the past bear 
testimony to the same thing. IN'eed I remind you of the great effort 
of scientific genius which our own time has witnessed — I mean the 
discovery of H^feptune. J^eed I remind you that it was no astronomical 
observer, no practical skill, which gave to us that great discovery. 
