Ill ADDRESS TO THE MATHEMATICAL AND PHYSICAL SECTIONS 



The most celebrated case of this kind is that of the corpuscular and the 

 undulatory theories of light. Up to a certain point the phenomena of light 

 are equally well explained by both ; beyond this point, one of them fails. 



To understand the true relation of these theories in that part of the field 

 where they seem equally applicable we must look at them in the light which 

 Hamilton has thrown upon them by his discovery that to every brachistochrone 

 problem there corresponds a problem of free motion, involving different velocities 

 and times, but resulting in the same geometrical path. Professor Tait has 

 written a very interesting paper on this subject. 



According to a theory of electricity which is making great progress in 

 Germany, two electrical particles act on one another directly at a distance, 

 hut with a force which, according to Weber, depends on their relative velocity, 

 and according to a theory hinted at by Gauss, and developed by Riemann, 

 Lorenz, and Neumann, acts not instantaneously, but after a time depending 

 on the distance. The power with which this theory, in the hands of these 

 eminent men, explains every kind of electrical phenomena must be studied in 

 order to be appreciated. 



Another theory of electricity, which I prefer, denies action at a distance 

 and attributes electric action to tensions and pressures in an all-pervading medium, 

 these stresses being the same in kind with those familiar to engineers, and the 

 medium being identical with that in which light is supposed to be propagated. 



Both these theories are found to explain not only the phenomena by the 

 aid of which they were originally constructed, but other phenomena, which 

 were not thought of or perhaps not known at the time ; and both have inde- 

 pendently arrived at the same numerical result, which gives the absolute 

 velocity of light in terms of electrical quantities. 



That theories apparently so fundamentally opposed should have so large 

 a field of truth common to both is a fact the philosophical importance of which 

 we cannot fully appreciate till we have reached a scientific altitude from which 

 the true relation between hypotheses so different can be seen. 



I shall only make one more remark on the relation between Mathematics 

 and Physics. In themselves, one is an operation of the mind, the other is a 

 dance of molecules. The molecules have laws of their own, some of which we 

 select as most intelligible to us and most amenable to our calculation. We 

 form a theory from these partial data, and we ascribe any deviation of the 

 actual phenomena from this theory to disturbing causes. At the same time we 



