52 Professor Thomson, Longitudinal Electric Waves, [Jan. 27, 



waves ; thus if there were any centre of disturbance to generate 

 waves whose length is comparable with molecular dimensions 

 longitudinal waves will spread through the dielectrics in the 

 variable field. 



Before proceeding to discuss mathematically the laws of pro- 

 pagation of these waves it may be of advantage to state some 

 of their peculiarities. We shall call the longitudinal waves due 

 to the motion of the charged atoms in a vacuum tube convective 

 waves, those due to the motion of the ether through a dielectric, 

 longitudinal dielectric waves ; these second waves might exist in 

 a vacuum tube along with the convective waves. In the first 

 place we notice that each of these classes of waves requires for its 

 propagation the presence of matter carrying electric charges as 

 well as ether ; longitudinal waves could not on Maxwell's theory be 

 propagated through pure ether. The wave length of the convec- 

 tive waves is not limited, while longitudinal dielectric waves can 

 only be transmitted when their wave lengths are comparable with 

 molecular dimension, and therefore are exceedingly small com- 

 pared with the lengths of the visible and ultra violet rays; the 

 finer the structure of the dielectric the more limited the range of 

 waves that can get through. The velocity of propagation of the 

 convective waves is equal to the velocity of translation of the 

 charged atoms, while that of the longitudinal dielectric waves is 

 equal to the velocity of the ether through the dielectric, this 

 velocity will depend upon the strength of the varying electric field 

 being larger in strong fields than in weak. If the ether moves 

 freely through the dielectric then its velocity will not change 

 abruptly in passing from one medium to another. Neither of 

 these waves produce any magnetic effects if they travel in the one 

 case in the direction of the moving atoms, in the second case in 

 that of the moving ether. 



We shall now proceed to find the equations which hold when 

 convective currents are present in the medium. 



We shall begin with the case of convective waves where the 

 convective currents are carried by moving charged atoms, and we 

 shall begin with the case when all the charged atoms, whatever 

 the sign of their charges, are moving with the same velocity : let 

 p, q, r denote the components of this velocity, X, Y, Z the com- 

 ponents of the electric intensity, a, ft, y the components of the 

 magnetic force; u, v, w the components of the total current, K the 

 specific inductive capacity of the medium, and /i its magnetic 

 permeability. 



Then p, the volume density of the electrification, is given by the 

 equation 



