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



which corresponds to a total outward flux over the sphere of 

 radius r amounting to 



f(/" 2 +*/'/") 



or simply 



2cf 



"2 



3 



at a great distance. 



On the general form of the new theory, the radiation 

 vector has components 



Sr = ~(f+rf'Hrf"+f% 



which corresponds to a total outward flux over the sphere of 

 radius r equal to 



^W + rf'+rff'+ff"), 



which vanishes at a great distance. 



Macdonald's own radiation vector corresponds to a radial 

 flux over the sphere r equal to 



f(/" 2 + 1 r /r)+Li(/'/" + ^ 2 > 



cf'*+±cfr'+rJ'f" 



which in the distant field reduces to 



cf"*+y'f". 



This agrees on the average with the result by Poynting's 

 theory if the field is oscillatory in character, but for the 

 particular case in which 



fa) = {ax + b) bl * + dx 



it would give no radiation at all ; in other cases, as for 

 instance when the acceleration of the moment of the doublet 

 is suddenly decreased, the radiation would be inwards towards 

 the doublet. 



