﻿Faraday-Tube 'Theory of Electro-Magnetism. 607 



Equating therefore expressions (45) and (47) and dividing 

 by d Xi we have 



or 



^7/_.. 2 ^ 2 y 



c 2 ^ 



.... (48) 



ot o% 



exhibiting the uniform propagation with velocity c inde- 

 pendent of the general motion of the tube. 



The relation between the electromagnetic disturbance and 

 the displacement y of the tube is easily seen to be given by 



V-e-K*'B* { } 



TT B.V j 



-£* ........ (50) 



But while in plane-polarized radiation the displacement of 

 the tube from its normal position is thus perpendicular to the 

 plane of polarization, in circularly polarized rays it is easy 

 to see that the reverse is the case. 



10. The intention in presenting the theory of Faraday 

 tubes in "the present form was to suggest possibilites of 

 modification which might explain various phenomena of 

 which no entirely satisfactory electrical explanation has been 

 given so far. 



In making attempts of this kind we may, for instance, take 

 advantage in various ways of the fact that the electric dis- 

 placement has been considered as a mean value taken over a 

 small, but not infinitesimal, area. From this point of view 

 the Maxwellian theory is microscopical, and a more micro- 

 scopical theory may be what is required in various regions 

 of modern physics. 



Again, the present theory rests on the localization of 

 electric and magnetic energy as functions of D and H and on 

 the derivation from these of equations of motion. Hence it 

 would be comparatively simple to estimate the effects either 

 of a modified distribution of energy, or of substituting any 

 different hypothesis for the principle of action. 



Lastly, quite a variety of hypotheses are possible as to the 

 exact nature of the electric particles. 



11. It will be observed that in describing the properties of 



