Energy in the Electrodynamic Field. 395 



which exhibits it as the combination of two parts : the first 

 term represents that part of the energy which balances 

 the potential energy of the field, whilst the second term 

 represents the energy dissipated by resistance. This 

 conforms generally with recognized ideas in these cases. 



On Macdonald's theory, however, the density of the 

 kinetic energy is given by 





which hardly admits of any physical explanation. 



Thus in a case like this, where there is actual dissipation, 

 the generalized theory takes full account of it and gives it 

 its proper expression, whilst Macdonald's theory ignores 

 it altogether. 



7. Up to this point the discussion has centred round a 

 discrimination between the different forms of the theory 

 alternative to Poynting^s theory, which is on an entirely 

 different plane. If we take these alternative theories 

 together we see that they possess one great advantage 

 over Poynting's theory, in so far as in them the electrons 

 occupy the more prominent positions, so that they should be 

 particularly appropriate in a purely relativist theory. In 

 fact, the particular formula expressing the magnetic energy 

 distribution specifies it explicitly in terms of the work 

 of the electric force acting on the electrons ; and the new 

 formula for the flux of energy shows that it is mainly the 

 flux of static potential energy of configuration of the 

 electrons themselves that is in reality under review. But 

 even in this respect the theories are not so complete in 

 the general case as might at first sight appear. In fact, 

 part of the magnetic energy still remains permanently 

 associated with the aether on account of the sethereal dis- 

 placement current, and this current also contributes a part 

 in the energy flux. 



There is, however, a very serious disadvantage attaching 

 to any of the new theories. They all involve in their 

 expression the scalar and vector potentials of the field, 

 the definition of which is mathematically incomplete and 

 uncertain. These functions cannot therefore, without 

 further arbitrary restrictions, be said to represent definite 

 physical entities, and a theory interpreted in terms of 

 them necessarily remains indefinite from the physical point 

 of view. Although this difficulty is a very serious one, 

 it may for the present be waived, because it does not appear 



