244 Prof. G. A. Schott on Bolirs Hypothesis 



for the energy flux. It will doubtless be admitted generally 

 that the retarded potentials represent those solutions of the 

 equations of the electromagnetic field which are specially 

 appropriate to the case of the accelerated electron. Hence 

 in order to remove the contradiction with Bohr's hypo- 

 thesis A, as it stands, only two alternatives appear to be 

 possible : either we must reject the Poynting flux, or we 

 must reject the retarded potentials together with the field 

 equations of which they are the appropriate solutions. 



3. Let us begin by considering the first alternative. It is 

 well-known that neither the Poynting flux, nor the usual 

 expressions for the energy densities, at any rate that for the 

 magnetic energy density, corresponding to it, are at all 

 unique. Livens * has recently examined this question in 

 detail and gives several possible expressions for the energy 

 flux, together with the corresponding ones for the magnetic 

 energy density. At the same time he arrives at the conclu- 

 sion that the Poynting energy flux and the classical energy 

 densities corresponding to it are to be preferred to all others 

 for physical reasons. It is, however, worthy of notice that 

 there is one form of the energy flux which is consistent with 

 Bohr's hypothesis A, viz. the expression <£C, where <£ denotes 

 the retarded scalar potential, and C the total electric currents 

 It follows from what Livens calls the Macdonald theory 

 generalized and corresponds to the magnetic energy density 



f(CrfA)/c, where A denotes the retarded vector potential. 

 This form for the energy flux, like the current C itself, is 

 transverse to the radius vector at an infinite distance from 

 the electron, and therefore merely gives rise to a flow of 

 energy along the wave-front and no radiation across it, being 

 fully consistent with Bohr's hypothesis A. 



4. Unfortunately, quite apart from the physical reasons 

 adduced by Livens, there are two strong reasons for pre- 

 ferring the Poynting energy flux to all other definitions of it. 



In the first place, the Poynting energy flux and the cor- 

 responding expression for the density of electromagnetic 

 momentum occupy a prominent place in the Theory of 

 Relativity, and it is difficult to see how such an expression 

 for the energy flux as that derived from the Macdonald 

 theory generalized can be used effectively in this connexion. 



Again, Lienard's expression for the radiation is perfectly 

 consistent with the electron mechanics founded on the ac- 

 cepted equations of the Electron theory, and this fact 

 constitutes a strong reason for preferring the Poynting flux,, 

 which is presupposed by Lienard's expression. 



* Livens, Phil. Mag. ser. 6, vol. xxxiv. p. 386 (1917). 



