1891.] On the Theory of Electrodynamics. 535 



by Maxwell.* It is necessary to emphasise that it is of the very 

 essence of a theory of this kind that the current in the dielectric is 

 not circuital, and, therefore, that the electric volume density pro- 

 duced by the electric displacement varies with the time. This is so 

 because the electrodynamic part of the electric force is not derived 

 from a potential. Any investigation which restricts the current to 

 be circuital is necessarily inconsistent with itself, except for the 

 limiting case which forms Maxwell's theory. 



A discrepancy of n per cent, (n a small number) between the 

 observed velocity and K 2 ~* would involve, by the formulae at the 

 beginning of this section, a difference of about 2n per cent, between 

 K 2 and K 2 1, so that K 2 would be of numerical magnitude about 

 100/2%; which determines the ratio in which the ordinary values of 

 the inductive capacities of all media, including vacuum, would have 

 to be multiplied, to make the polarisation theory not discordant with 

 the observations. 



The amount of discontinuity in* the current at the surface of a 

 conductor is the fraction K 2 -1 of the total current across the surface. 

 At the interface between two dielectric media, denoted by the values 

 K 2 and K' 2 , the normal components - of the displacement -on the two 

 sides are 



(K 2 l)N/47r and (K' a 

 where N, N' are the normal components of the electric force, so that 



'K 2 N = K' 2 N'. 



Thus the discontinuity in the displacement is ' (N' N)/4?r or 

 (K 2 /K' 2 ^-l)N/47r compared with a total displacement (K 2 l)N/4jr; 

 the ratio of these is (K 2 K' 2 )/K' 2 (K 2 1), which is less than the 

 fraction K' 2 -1 , which corresponds to the surface of a conductor. 



Thus, under the assumed circumstances/ the ratio of the amplitudes 

 of the condensational waves to those of the transverse waves would 

 have a superior limit of the order 1 2/100; in the observations quoted 

 this limit is at 5 per cent. 



It is worth while to emphasise that if the polarisation theory were 

 to take K 2 equal to unity for a vacuum, K! would be zero, and in a 

 vacuum there would be nothing but action at a distance. It is thus 

 an essential part of a theory like this that a vacuum has an absolute 

 inductive capacity greater than unity, so that the ordinary value 

 unity is merely a relative unit. Thus the transition to Maxwell's 

 scheme, where the absolute coefficients are all assumed infinite, does 

 not involve any undue stretch of the original hypothesis. 



In the above, the relative velocities in different media of the 



* Cf. J. J. Thomson, ' Brit. Assoc. Keport,' 1885, p. 140. 



