Equations in a Homogeneous Isotropic Medium. 49 



the potential on one side of the plane is made greater by the 

 amounts (tensor of e) than on the other side. Say ^ = ^6 

 and — ^e. Thus we have instantaneous propagation of '^ to 

 infinity. I prefer, however, to say that this is only a mathe- 

 matical fiction, that nothing is propagated at all, that the 

 electromagnetic mechanism is of such a nature that the ap- 

 plied forces are balanced on the spot, that is, in the sheet, by 

 the reactions. 



To emphasize this again, let the sheet be not infinite, but 

 have a circular boundary. Let the medium be of uniform 

 inductivity fju, and permittivity c. Then, irrespective of its 

 conductivity, disturbances ai'e propagated at speed i?=(/ac)~*, 

 and their source is the vortex-line of e, on the edge of the 

 disk. At any time t less than ajv, where a is the radius of 

 the disk, the disturbance is confined within a ring whose axis 

 is the vortex-line. Everywhere else E = and H = 0. On 

 the surface of the ring, E=/ArH, and E and H are perpendi- 

 cular ; there can .be no normal component of either. 



Now we can naturally explain the absence of any flux in 

 the central portion of the disk by the aj)plied forces being 

 balanced by the reactions on the spot, until the wave arrives 

 from the vortex-line. But how can vve explain it in terms of 

 '^, seeing that '^ has now to change by the amount e at the 

 disk, and yet be continuous everywhere else outside the ring ? 

 We cannot do it, so the propagation of ^ fails altogether. 

 Yet the actions involved must be the same whether the disk 

 be small or infinitely great. We must therefore give up the 

 idea altogether of the propagation of a '^ to balance impressed 

 force. In the ring itself, however, we may regard the pro- 

 pagation of '^ (a different one) , A, and A ; or, more simply, 

 of E and H, 



If there be no conductivity, the steady electric field is 

 assumed anywhere the moment the two waves from opposite 

 ends of a diameter of the disk coexist ; that is, as soon as the 

 wave arrives from the more distant end (Phil. Mag. May 

 ISSS"^). But this simplicity is quite exceptional, and seems 

 to be confined to plane and spherical waves. In general 

 there is a subsidence to the steady state after the initial 

 phenomena. 



If it be remarked that incompressibility (or something equi- 

 valent or resembling it) is needed in order that the medium 

 may behave as described {%. e. no flux except at the vortex- 

 line initially), and that if the medium be compressible we 

 shall have other results (a pressural wave, for example, from 

 the disk generally), the answer is that this is a wholly inde- 

 * "Electromagnetic Waves," § 25. 



Phil. Mag. S. 5. Vol. 27. No. 164. Jan. 1889. E 



