316 REPORT—1905. 
cited as instances that are occupying present activities, not to speak of radium, 
the unfolding of whose future is watched by eager minds. 
One gap, indeed, in this subject strikes me. There are great histories of 
mathematics and great histories of astronomy; I can find no history of physics 
on the grand scale. Some serviceable manuals there are, as well as monographs 
on particular topics; what seems to me to be lacking is some comprehensive and 
comparative survey of the whole range. The history of any of the natural 
sciences, like the history of human activity, is not merely an encyclopedic record 
of past facts; if reveals both the spirit and the wealth which the past has be- 
queathed to the present, and which, in due course, the present will influence before 
transmission to the future. Perhaps all our physicists are too busy to spare the 
labour needed for the production of a comprehensive history; yet I cannot help 
thinking that such a contribution to the subject would be of great value, not to 
physicists alone. 
But, as you hear me thus referring to astronomy and to physics, some of you 
may think of the old Roman proverb which bade the cobbler not to look above his 
last; so I take the opportunity of referring very briefly to my own subject. 
One of the features of the century has been the continued development of 
mathematics. As a means of calculation the subject was developed as widely 
during the earlier portion of the century as during the preceding century ; it 
soon began to show signs of emergence as an independent science, and the latter 
part of the century has witnessed the emancipation of pure mathematics. It 
was pointed out, in connection with the growth of theoretical astronomy, 
that mathematics developed in the direction of its application to that subject. 
When the wonderful school of French physicists, composed of Monge, 
Carnot, Fourier, Poisson, Poinsot, Ampére, and Fresnel (to mention only some 
names), together with Gauss, Kirchhoff, and von Helmholtz in Germany, and 
Ivory, Green, Stokes, Maxwell, and others in England, applied their mathematics 
to various branches of physics, for the most part its development was that of an 
ancillary subject. The result is the superb body of knowledge that may be 
summarised under the title of ‘mathematical physics’; but the final interest is 
the interest of physics, though the construction has been the service of mathe- 
matics. Moreover, this tendency was deliberate, and was avowed in no uncertain 
tone. Thus Fourier could praise the utility of mathematics by declaring that 
‘there was no language more universal or simpler, more free from errors or 
obscurity, more worthy of expressing the unchanging relations of natural 
entities’; in a burst of enthusiasm he declares that, from the point of view he 
had indicated, ‘mathematical analysis is as wide as Nature herself, and ‘it 
increases and grows incessantly stronger amid all the changes and errors of the 
human mind.’ Mathematicians might almost blush with conscious pleasure at 
such a laudation fo their subject from such a quarter, though it errs both by 
excess and defect; but the exultation of spirit need not last long. The same 
authority, when officially expounding to the French Academy the work of Jacobi 
and of Abel upon elliptic functions, expressed his chilling opinion (it had 
nothing to do with the case) that ‘the questions of natural philosophy, which 
have the mathematical studyfo all important phenomena for their aim, are also 
a worthy and principal subject for the meditations of geometers. It is to be 
desired that those persons who are best fitted to improve the science of calcula- 
tion should direct their labours to these important applications.’ Abel was soon to 
pass beyond the range of admonition ; but Jacobi, in a private letter to Legendre, 
protested that the scope of the science was not to be limited to the explanation 
of natural phenomena. I have not quoted these extracts by way of even hint of 
reproach against the author of such a wonderful creation as Fourier’s analytical 
theory of heat; his estimate could have been justified on a merely historical 
review of the circumstances of his own time and of past times; and I am not 
sure that his estimate has not its exponents at the present day. But all history 
shows that new discoveries and new methods can spread to issues wider than those 
of their origins, and that it is almost a duty of human intelligence to recognise 
this possibility in the domain of progressive studies, The fact is that mathe- 
