4.2.4, REPORT—-1904, 
work of the later school is its increasing relation to and association with experi- 
ment. In the days when the chief applications of Mathematics were to the pro- 
blems of Gravitational Astronomy, the mathematician might well take his materials 
at second hand ; and in some respects the division of labour was, and still may be, 
of advantage. The same thing holds ina measure of the problems of ordinary 
Dynamics, where some practical knowledge of the subject-matter is within the 
reach of everyone. But when we pass to the more recondite phenomena of 
Physical Optics, Acoustics, and Electricity, it hardly needs the demonstrations 
which have involuntarily been given to show that the theoretical treatment 
must tend to degenerate into the pursuit of academic subtleties unless it is con- 
stantly vivified by direct contact with reality. Stokes, at all events, with little 
guidance or encouragement from his immediate environment, made himself from 
the first practically acquainted with the subjects he treated. Generations of 
Cambridge students recall the enthusiasm which characterised his experimental 
demonstrations in Optics, These appealed to us all; but some of us, I am afraid, 
under the influence of the academic ideas of the time, thought it a little unneces- 
sary to show practically that the height of the lecture-room could be measured by 
the barometer, or to verify the calculated period of oscillation of water in a tank 
by actually timing the waves with the help of the image of a candle-flame 
reflected at the surface. 
The practical character of the mathematical work of Stokes and his followers 
is shown especially in the constant effort to reduce the solution of a physical 
problem to a quantitative form. A conspicuous instance is furnished by the 
labour and skill which he devoted, from this point of view, to the theory of the 
Bessel’s Function, which presents itself so frequently in important questions of 
Optics, Electricity, and Acoustics, but is so refractory to ordinary methods of 
treatment. It is now generally accepted that an analytical solution of a physical 
* question, however elegant it may be made to appear by means of a judicious nota- 
tion, is not complete so long as the results are given merely in terms of functions 
defined by infinite series or definite integrals, and cannot be exhibited in a 
numerical or graphical form. This view did not originate, of course, with 
Stokes; it is clearly indicated, for instance, in the works of Fourier and Poinsot, 
but no previous writer had, I think, acted upon it so consistently and thoroughly. 
We have had so many striking examples of the fruitfulness of the combination 
of great mathematical and experimental powers that the question may well be 
raised, whether there is any longer a reason for maintaining in our’minds a dis- 
tinction between mathematical and experimental physics, or at all events whether 
these should be looked upon as separate provinces which may conveniently be 
assigned to different sets of labourers. It may be held that the highest physical 
research will demand in the future the possession of both kinds of faculty, We 
must be careful, however, how we erect barriers which would exclude a Lagrange 
on the one side or a Faraday on the other. There are many mansions in the 
palace of physical science, and work for various types of mind. A zealous, or over- 
zealous, mathematician might indeed make out something of a case if he were to 
contend that, after all, the greatest work of such men as Stokes, Kirchhoff, and 
Maxwell was mathematical rather than experimental in its complexion. An 
argument which asks us to leave out of account such things as the investigation of 
Fluorescence, the discovery of Spectrum Analysis, and the measurement of the 
Viscosity of Gases, may well seem audacious; but a survey of the collected works of 
these writers will show how much, of the very highest quality and import, would 
remain. However this may be, the essential point, which cannot, I think, be con- 
tested, is this, that if these men had been condemned and restricted to a mere 
book knowledge of the subjects which they have treated with such marvellous 
analytical ability, the very soul of their work would have been taken away. I 
have ventured to dwell upon this point because, although I am myself disposed to 
plead for the continued recognition of mathematical physics as a fairly separate 
field, I feel strongly that the traditional kind of education given to our professed 
mathematical students does not tend to its most effectual cultivation. This 
education is apt to be one-sided, and too much divorced from the study of tangible 
