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VII. On the Fundamental Formulations of Flech^odynamics. 
By G. H. Livens, University of Manchester. 
Communicated by W. M. Hicks, F.R.S. 
Eeceived March 14,—Read June 26, 1919. 
1, Modeen electrical theory based on Maxwell’s concept of an aethereal 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 Poynting’s form* * * § of the theory is the only one conceivable. A single 
alternative has on one occasionf 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.^ This view appears 
to have originated with the idea that the magnetic force is the fundamental mthereal 
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. 
X This is the view of practically all Continental writers on this subject. 
§ Cf. ‘Roy. Soc. Proc.,’ A, vol. 93, p. 20 (1916). 
VOL. ccxx. — A 577. 2 g 
[Published March 17, 1920. 
