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VII. On the Fundamental Formulations of Electrodynamics. 



By G. H. LIVENS, University of Manchester. 



Communicated by W. M. HICKS, F.R.S. 



Eeceived March 14, Read June 26, 1919. 



1. MODERN electrical theory based on MAXWELL'S concept of an sethereal displacement 

 current, is generally regarded as being sufficiently complete in itself to cover all 

 actions so far revealed to us, if we exclude those intra-atomic phenomena which 

 probably involve some additional but not necessarily inconsistent action in their 

 working. There, still, however exists a good deal of uncertainty as to the actual 

 results of the development of this theory in certain directions, and no account has yet 

 been taken of the great degree of latitude allowed by it in its simplest and most 

 general form. For example, in most presentations of the theory of energy streaming 

 in the electromagnetic field the discussion is given in a way which might lead one to 

 believe that POYNTINQ'S form* of the theory is the only one conceivable. A single 

 alternative has on one occasion! been suggested, but rather as an improvement on 

 POYNTING'S form than as an indication of its uncertainty. Whilst it cannot be denied 

 that POYNTING'S theory is probably the most appropriate one yet formulated, yet it 

 must be recognised that there are an infinite number of fundamentally different forms 

 each of which is itself perfectly consistent with MAXWELL'S theory as expressed in his 

 differential equations of electromagnetic interaction. 



Again, but now we are on a different plane, it has usually been stated that 

 MAXWELL'S theory is not of sufficient generality to cover the cases where there exists 

 the complication of non-linear induction in ferromagnetic media.J This view appears 

 to have originated with the idea that the magnetic force is the fundamental sethereal 

 vector of the magnetic field, whereas, as a matter of fact, the only consistent view 

 of the energy relations of such a field leads to the conclusion that the magnetic 

 induction is the true sethereal vector, the magnetic force being an auxiliary vector 



* 'Phil. Trans.,' A, vol. 175 (1884). 

 t MACDONALD, ' Electric Waves,' Chs. IV., V., VIII. 

 \ This is the view of practically all Continental writers on this subject. 

 Of. 'Roy. Soc. Proc.,' A, vol. 93, p. 20 (1916). 

 VOL. CCXX. A 577. 2 G [Published March 17, 1920. 



