14:4 Mr. E. A. Biedermann on the Energy 



would be equivalent. It was precisely the apparent dis- 

 crepancy between these two expressions which led me to put 

 forward the modification of the usual expression for the 

 magnetic energy density. 



If Mr. Livens can show that the above relation — a purely 

 geometrical one — actually is true, so that (7) and (8) in reality 

 are equivalent, there would be an end of the matter, and it 

 would only remain for me to apologize for having raised the 

 issue at all ; but it certainly does not seem sufficient merely 

 to say that we must assume it to be so, — for that, in fact, 

 is what the assumption that divA = at all points really 

 amounts to. I further suggested some reasons as to why 

 expressions (7) and (8) were apparently not equivalent — in 

 other words, why div A does not vanish at all points, — and 

 showed that this only occurred when the moving charge 

 constituting the current was distributed continuously 

 throughout the substance of the conductor instead of being, 

 as it actually is, concentrated in discrete particles. 



Mr. Livens, 1 think, is under some misapprehension as to 

 the generality I have attributed to the expression for T — a 

 misunderstanding for which I am myself to blame. On 

 p. 152 of my paper I said " It is suggested, therefore, that 

 this (i. e. (H 2 -f G 2 )/87r) may be a correct representation in all 

 cases." I should have said "in all cases for which the 

 original expressions for H and G hold good, namely all cases 

 of slow uniform motion of the charges." Mr. Livens's 

 further criticism still applies, however, and amount? to this 

 — that because 



for the special case of two closed linear circuits, I have 

 assumed the expression on the right to be the correct general 

 expression for the magnetic energy, which would, of course, be 

 a most unwarrantable conclusion. Actually my argument 



was, in effect, that because o— K 2 dv for the special case 



apparently does not equal the above expression, but is 

 equal to 



^.{ S ^ + ' 222 ^(^)}- 8 y'(divA) 



2 dv, 



