14-2 Mr. E. A. Biedermann on the Energy 



Failure of Petrini's generalization. 



It is easily seen from (B) that Professor Petrini's 

 generalization fails for the Case II. For 



+ oos(log i+ logi + tan- i) + cos(log * + tan" 1 i)}], 



which exists only for special values of a, /3. In fact, 

 the necessary conditions for the existence of /\V are the 

 following : — 



1 + cos y log ~ V-f cos (log 7s ) = in the limit, 



sin Hog - j -f sin (log -~) = in the limit. 

 When these conditions are satisfied, /\Y = 0. Thus ^V 



exists (and is zero) only when, in the limit, y and — 3 are of 

 the forms "i h i 



(2^±|) ( 2n .+f) 



e K 3 and £ V 3 y 

 respectively, ?n and t?, being any integers. 



XIII. On the Energy in the Electromagnetic Field.^ 



To the Editors of the Philosophical Magazine. 



r|„ 1T1 a,™ Bedford, 



Dear bins,— March mh? ' 1917< 



IN your March number Mr. G. H. Livens strongly 

 criticises my reasons for putting forward the modified 

 expression {H 2 + (div A) 2 }8-7r for the magnetic energy density 

 in an electromagnetic field, and says that my argument is 

 convincing only when divA = — that is to say, that it is 

 entirely unconvincing. Mr. Livens obtains for the magnetic 

 energy the expression 



~ f HVr = it — (V + v r 2 + w 2) 



07T ) a r 



-t- VT e ^- s (,i r y s -r v r v 8 + w r w s ) - ~ I (div A) 2 dv, 



