398 Mr. G. H. Livens on the Flux of 



would vanish at all points of the field. In any other case, 

 when (f> does not vanish, the transfer would merely take 

 place parallel to the main component of the current, which 

 is generally parallel to the electric force in the field, and 

 would therefore be perpendicular to the direction of propa- 

 gation of the radiation itself. 



Even on Macdonald's theory this conclusion is not 

 appreciably affected. For in that case the radiation 

 vector is 



-and in the present case this is 



sOW.+isW) 



in A m 2(int—a+ibz+ie m ) A„ t d j 2(int-a+ibz+i9j 



4tt a-\-ib $7r(a + ib) dt 



0: 



>\ 



so that again there is no flux of energy in any direction. 



Of course this is the only result we could expect in a field 

 where the total energy at each point is zero, or at most equal 

 to the energy developed as heat in the medium, which can 

 under no circumstances be propagated from one point of the 

 field to another except by means outside the electromagnetic 

 scheme. 



Whether such a view of the processes in operation in 

 radiation fields is physically valid or not, it is difficult to 

 say : it would certainly lead to new complications in optical 

 theory, where the idea of the transfer of energy along a beam 

 of light is fundamental, but this cannot be regarded as a 

 proper reason for ruling it out altogether. The only method 

 we have of probing such fields is to examine their effect on 

 matter, and in the neighbourhood of all matter the simple 

 circumstances assumed above cease to be valid, and the 

 dynamics of the interaction between the sether and electrons 

 assumes fundamental importance. It will therefore be 

 necessary to inquire further into the problem of the 

 generation and absorption of radiation by electrons before 

 progress can be made in the discussion. 



9. We next consider the circumstances in the electro- 

 magnetic field surrounding a simple Hertzian vibrator of 

 strength f(ci) at time t. The complete circumstances of this 

 field are well known, and in the simplest case of a first-order 



