242 MR. G. H. LIVENS ON THE 



change of momentum, so that we are rather forced to regard these outstanding terms 

 as pointing to the failure of the ideas from which we set out. This conclusion does 

 not, of course, invalidate the results derived in the simpler electron theory, as the 

 concept of momentum will remain under the simplest conditions as a convenient 

 mathematical expression for the actual result, whatever be its ultimate physical basis. 

 The present formulation possesses another disadvantage which is apparently not 

 inherent in the simplest presentations of the momentum idea. In the electron theory, 

 as usually developed, the momentum remains as a fundamental quantity and is 

 distributed over the field with the density 



J- [EB] 



47TC 



at each point ; this gives it a purely sethereal constitution as the vectors E and B are 

 those which define the conditions in the sethereal field. In the present formulation 

 the vector B is replaced by the vector H which is essentially an auxiliary mechanical 

 vector in the theory ; the fundamental nature of the momentum vector is therefore 

 entirely lost. We can, of course, assume that some of the momentum is in reality 

 attached to the matter, and such an assumption has certain points in its favour. 

 The force of electromagnetic origin on the dielectric media for example has an 

 x component which per unit volume is 



(?} + l 

 \ dx / c 



and this may be written in the form 



P |E) + i( [Pa ^ + l| 



H'*' / /> \ W / f* r/f 



CJC / C \ CJL I V LX/v 



The first two terms appear as those appropriate to the energy function in the 

 statical theory which would be 



so that the third might be regarded as a kinetic reaction to a rate of change of 

 momentum, which would be distributed throughout the medium with a density 



1[PB] 

 at each point. 



A similar analysis and analogous results hold for the magnetic media. 



There is, too, a relation satisfied by the momentum vector which appears in the 

 simplest form of the theory and to which a fundamental significance is attached by 



