in the Electromagnetic Field. 145 



where the integral apparently does not vanish, therefore the 

 general expression for T should be 



*J 



07T 



for the limited condition of: slow uniform motion. For this 

 condition divA = G, and 



cjc* + ■■>*- i { ^ + «**?&*) } • 



On p. 154 I expressly pointed out that expression (13) 

 could not be regarded as of complete generality, since it was 

 derived from others for H and G, which took no account of: 

 the finite velocity of propagation, and, I might have added, 

 expressions which were strictly true only for slow uniform 

 motions. 



Neither did I intend to imply that 22 — was to be 



regarded as a complete expression of the potential energy- 

 It is clear that the complete specification of the kinetic and 

 potential energy explicitly in terms of the charges, their 

 distances, velocities, and accelerations, would of: necessity 

 have to include the whole previous history of their motions. 

 All that I showed in the remainder of the paper was that 

 the general equations of the field were obtained from the 

 limited special form of the kinetic potential of the system by 

 substituting [p] for p, \_pu\ for pu, &c, and on p. 156 I 

 pointed out that this could not be regarded as an independent 

 derivation of these equations, — in fact that, as Mr. Livens 

 says, it was not a method susceptible of strict mathematical 

 specification. Finally, from a comparison of the general 

 form of the expressions for H with the particular form 

 assumed by these in the case of slow uniform motion, together 

 with the form assigned to the expression f or G under the 

 same conditions, I concluded that the most general expression 

 for G was divA; so that the most general expression for the 

 magnetic energy density was 



i (H 2 + G 2 ) = i{(curlA) 2 + (div A 2 )}. 



07T 07T 



This expression would, of course, only reduce to (13) under 

 the limitations mentioned. 



The crux of the whole matter, then, lies in the equivalence 



Phil. Mag. S. 6. Vol. 34. No. 200. Aug. 1917. L 



