PRESIDENT’S ADDRESS. 7 
made; for example, electric waves were discovered by mathematics long 
before they were detected in the laboratory. He has also at his 
command a language clear, concise, and universal, and there is no 
better way of detecting ambiguities and discrepancies in his ideas than 
by trying to express them in this language. Again, it often happens 
that we are not able to appreciate the full significance of some physica] 
discovery until we have subjected it to mathematical treatment, when 
we find that the effect we have discovered involves other effects which 
have not been detected, and we are able by this means to duplicate 
the discovery. Thus James Thomson, starting from the fact that 
ice floats on water, showed that it follows by mathematics that ice 
can be melted and water prevented from freezing by pressure. This 
effect, which was at that time unknown, was afterwards verified by 
his brother, Lord Kelvin. Multitudes of similar duplication of physical 
discoveries by mathematics could be quoted. 
I have been pleading in the interests of physics for a greater study 
of mathematics by physicists. I would also plead for a greater study 
of physics by mathematicians in the interest of pure mathematics. 
The history of pure mathematics shows that many of the most 
important branches of the subject have arisen from the attempts made 
to get a mathematical solution of a problem suggested by physics. 
Thus the differential calculus arose from attempts to deal with the 
problem of moving bodies. Fourier’s theorem resulted from attempts 
to deal with the vibrations of strings and the conduction of heat; 
indeed, it would seem that the most fruitful crop of scientific ideas 
is produced by cross-fertilisation between the mind and some definite 
fact, and that the mind by itself is comparatively unproductive. 
I think, if we could trace the origin of some of our most comprehen- 
sive and important scientific ideas, it would be found that they arose 
in the attempt to find an explanation of some apparently trivial and 
very special phenomenon; when once started the ideas grew to such 
generality and importance that their modest origin could hardly be 
suspected. Water vapour we know will refuse to condense into rain 
unless there are particles of dust to form nuclei; so an idea before 
taking shape seems to require a nucleus of solid fact round which it 
can condense. 
I have ventured to urge the closer union between mathematics and 
physics, because I think of late years there has been some tendency 
for these sciences to drift apart, and that the workers in applied 
mathematics are relatively fewer than they were some years ago. This 
is no doubt due to some extent to the remarkable developments made in 
the last few years in experimental physics on the one hand and in the 
most abstract and metaphysical parts of pure mathematics on the other. 
The fascination of these has drawn workers to the frontiers of these 
regions who would otherwise have worked nearer the junction of the 
