MATHEMATICAL PHYSICS. 511 



tact with reality. Stokes, at all events, with little guidance or encour- 

 agement from his immediate environment, made himself from the first 

 practically acquainted with the subjects he treated. Generations of 

 Cambridge students recall the enthusiasm which characterized his ex- 

 perimental 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 unnecessary 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 solu- 

 tion of a physical problem to a quantitative form. A conspicuous in- 

 stance is furnished by the labor and skill which he devoted, from this 

 point of view, to the theory of the BessePs 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 notation, is not complete so long as the results are given 

 merely in terms of functions defined by infinite series or definite inte- 

 grals, and can not 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 distinction between mathematical and ex- 

 perimental physics, or at all events whether these should be looked 

 upon as separate provinces which may conveniently be assigned to dif- 

 ferent sets of laborers. 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 Max- 

 well 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 seeem audacious ; but a 



