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



case concerned more directly with radiation phenomena. 

 Although it cannot be said that the theory explains directly 

 all the observable phenomena in the field that it covers, yet 

 its peculiar appropriateness in those cases where it does 

 apply almost compels us to the view, now almost exclusively 

 held, that it represents a generally valid expression of the 

 physical processes involved. 



It has, however, been pointed out by Macdonald * that 

 the expression adopted by Poynting for the magnetic energy 

 density is not the one which properly belongs to Maxwell's 

 own form of electrodyuamic theory; and that, in con- 

 sequence^ the specification of the energy flux in the field 

 given by Poynting is not really consistent with that theory. 

 By using a form of the expression for the magnetic energy 

 in terms of the vector potential and current distribution, 

 which is equivalent to that used by Maxwell in the special 

 case he examines, he obtains a new specification of the 

 energy streaming which gives it as determined by a vector 

 differing from Poynting's vector by the additional term 



A being the vector potential of the field. 



Although Macdonald's objection to the first form of 

 expression for the magnetic energy density has been sub- 

 sequently removed by the establishment of the equal validity 

 of that form in a dynamical theory, it appears that his 

 suggested modification of the theory of energy streaming 

 is at least consistent with a logical formulation of the 

 mathematical relations of the electromagnetic field, and 

 deserves in consequence more consideration than has appa- 

 rently been devoted to it. Beyond the short discussion 

 given by its author, nothing seems to have been done to 

 examine the possibilities of the theory, although Blake and 

 Fountain claim to have obtained experimental evidence in 

 its favour. 



The investigation outlined in the present paper was under- 

 taken, partly with a view to placing the new theory on a 

 precise theoretical basis under more general circumstances 

 than are considered by Macdonald, but mainly with the idea 

 of examining it in sufficient detail to obtain an estimate of 

 its possibilities as an alternative to Poynting's theory. 



At the outset the basis of the theory of energy streaming 

 in the general electromagnetic field is briefly reviewed and 

 the most general form of Poynting's and Macdonald's 

 * < Electric Wayes,' 1902. 



