1891.] electrical waves in dielectric media. 165 



when the circuits are not assumed to be complete was then 

 examined mathematically on the lines of v. Helmholtz's investiga- 

 tions. It was shown that waves of transverse displacement will 

 always be propagated in a dielectric, irrespective of what hypo- 

 thesis is assumed as to the law of the mutual action of incomplete 

 currents, whether that adopted by v. Helmholtz or the still 

 more general one which is formally possible. But it was also 

 shown that, if the velocity of these waves in a non-magnetic 

 dielectric is equal to the inverse square root of the specific 

 inductive capacity, the currents are necessarily complete. The ex- 

 perimental evidence is strongly in favour of this relation, and in 

 so far constitutes a demonstration of Maxwell's theory of electro- 

 dynamic action and its mode of propagation in stationary media 1 . 



(2) A mechanical representation of a vibrating electrical system, 

 and its radiation. By J. Larmor, M.A., St John's College. 



The propagation of undulations of electric polarisation in a 

 dielectric is exactly similar to the propagation of elastic waves 

 in a solid medium, which must be absolutely incompressible if 

 we follow Maxwell's scheme, but may transmit waves of con- 

 densation as well as shearing waves if we admit the more general 

 scheme developed by von Helmholtz. 



The propagation of electrical actions in a medium which is a 

 conductor of ordinary type (so that the number which expresses its 

 inductive capacity in C.G.S. electromagnetic measure is very small, 

 while that which expresses its specific resistance is large) follows 

 the same law as the diffusion of heat in a conducting medium, 

 with the proviso that the thermal diffusivity is to be proportional 

 to the reciprocal of the electric conductivity. For this reason 

 rapidly alternating disturbances in the medium surrounding a 

 conducting mass are only transmitted skin deep into the con- 

 ductor, the depth of this skin diminishing with increasing rapidity 

 of the alternations and increasing conductivity, in the same manner 

 as in the corresponding question of the propagation beneath 

 the surface of the ground of the daily and annual alternations of 

 temperature. For this reason also a sheet of conducting metal acts 

 as a screen against alternating electrodynamic influence. 



In development of this elastic solid analogy it has recently 

 been explained by Sir W. Thomson 2 that the magnetic induction 

 due to a steady electric current traversing a circuital channel 

 in the medium is represented by twice the vorticity of the elastic 

 strain when a longitudinal force of amount represented by the 

 current is applied to the portion of the medium which coincides 

 with this channel. 



1 See Proc. Roy. Soc. 1891, Vol. xlix., p. 521. 



2 Math, and Phys. Papers, Vol. in. p. 451. 



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