1885.] equations of vibrations of ether in a light wave. 295 



The stress would in this case be along the lines of the electro- 

 magnetic momentum. All that can be said in favour of this 

 analogy is, that it shews such agreement as is proved in Mr Glaze- 

 brook's paper {Phil. Mag., June, 1881). 



(3) I shall work out one other case, because, though not at 

 first sight a desirable one, it appears to find some support from 

 Maxwell. 



Put v%=n /OK . 



therefore v% = u J 



fd% dr}\ _ dh dg 

 \dy dz) dy dz ' 

 which plays no part in the electro-magnetic theory 

 fdt, drf\ _dw dv _ 

 \dy dz) dy dz ' 

 which is also without importance. 



Let (£ i], £) and (£ , rj Q , £ ) be the velocities of two separate 

 disturbances in the medium, then the term which will appear in 

 the kinetic energy in which these velocities are connected is 



(IL+vvo+it)- 



Putting z/£ = u, etc., taking the triple integral over all space 

 and transforming, neglecting the surface integrals, we get 



- IIKL U + Vo v + t w ) dxdydz 



=viwi-i)^(i-i)^(s-iF^ 



Comparing this with Maxwell's provisional theory of the mag- 

 netic action on light {Electricity and Magnetism, Vol. II. §§ 824, 

 825), we see that the latent analogy underlying his hypothesis is 

 that which is given above. 



On this analogy the electric displacement would be propor- 

 tional to the actual displacement. The electro-magnetic momentum 

 and magnetic induction would become mere mathematical ex- 

 pressions. The electromagnetic and electro-static energies could 

 still be proved equal, the electro-static energy being now pro- 

 portional to the intensity of the light. The only merit of this 

 supposition appears to be that it is the basis of Maxwell's specu- 

 lations. 



