1885.] equations of vibrations of ether in a light wave. 293 



which equations agree with those of Maxwell (Vol. II., Art, 643), 

 and lead me to suggest that the true stress due to strain is 

 the tension along the lines of magnetic force and that the hydro- 

 static pressure is due to the velocities. The stress being made up 

 of two parts just as the energy is made up of two parts. 



6. I have taken above the variations of the actual displace- 

 ment as proportional to the magnetic force, so that the electro- 

 magnetic energy is proportional to the kinetic. But as this is an 

 open question, I will work out some other analogies. 



(1) Put v% = F, vr\ = G, v%= H, that is f, rj, £ proportional to 

 the components of the vector potential 



\dX_ohfl 

 \dy dz 



fjb r X = v 



etc. 



» kv dP , 



(23). 



Hence kinetic energy = -p- 2 [f 2 + g 2 + h 2 }, 



potential energy 



Put 



kinetic energy 



potential energy 



1 k 



a 2 fjb 2 k 



(a 2 + /3 2 + 7 2 ) 



_ Jt_ 



iL(a 2 + /3 2 + T 2 ). 



The result of this analogy is to interchange the kinetic and 

 potential energies, but the stresses in the medium would be along 

 the lines of the electric displacement instead of magnetic force. 

 The form of the vector here representing a might, at first sight, 

 appear the more suitable, but the vector whose components are 



7c* 7 



~r- — ~r , etc., has in our case no more rotational property than has 



In neither case do (a, /3, 7) or (/, g, h) appear to have the 

 proper dimensions, but the relative dimensions are of course correct 

 on either supposition. In order to make the dimensions correct, 



