130 Mr Glazebrooh, A comparison of Maxwell's [Feb. 25, 



Now Maxwell concludes that y 2 ^ is proportional to the volume 

 density of free electricity. This is of course the case if there is no 

 electromagnetic induction, but when it exists we have (p being the 

 volume density) on his theory 



df dh dg K ( ,_ dJ\ ,_.. 



and if we suppose with Maxwell that, the medium being an in- 

 sulator, -~ = we get 



dt 



dt vil = ~W 



exactly the same equation as that which flows from Helmholtz's 

 theory by putting <I> = and — /xk -j- = J. 



We have already noticed that Helmholtz states that his theory 

 reduces to Maxwell's by putting k = 0. He arrives at this result 

 by considering the normal wave which does not exist on Maxwell's 

 theory, and states that according to Maxwell its velocity is infinite. 



The comparison between the two theories shews us that they will 

 be reconciled if we put -j- = everywhere. If it be a part of 



Maxwell's theory that J should not be zero, theu since J= — fik—j- 



we must have k infinite and not zero, and we obtain Maxwell's 

 relation between J and O ; while the normal wave of Helmholtz' 

 theory disappears, its velocity becoming zero. 



If however we assume that J= is an essential condition of 

 Maxwell's theory the two are reconciled independently of the 



value of k by the supposition that -j- = and the normal wave 



depending on <E> disappears. 



[Note added August, 1884.] 



Since the above was in type Mr J. J. Thomson has pointed 

 out to me that the supposition k = co will make the action, on 

 Helmholtz' theory, of one element of current on another infinite. 



