Least Action in the Theory of Electrodynamics. 199 1 

 whilst for each electron there are three equations of type 



dt\d<c/ o^x 



![ e OorlA].+ ^ + .|*-0. 



c L J c ot ox 



With the exception of the second equation, these are 

 identical with Larmor's equations deduced from the older 

 alternative basis. It thus appears that the dynamical 

 equations determining the strain conditions of the asther 

 and the motion of the various electrons are identical on 

 either form of the theory. 



It also appears that the scalar and vector multipliers <j> 

 and A, which were originally introduced into the theory as 

 undetermined functions, are, in fact, the scalar and vector 

 potentials of Maxwell's theory ; but they are here relegated 

 to their proper position as auxiliary functions introduced to 

 procure analytical simplicity in the relations of the theory, 

 and are so far without direct physical significance. 



The present discussion does not, of course, help in the 

 elucidation of any difficulties experienced in considering a 

 definite choice of one of the specified forms for the magnetic 

 energy distribution and the consequent rejection of the 

 other, except in so far as it has removed one of the difficulties 

 in the way of a general acceptance of the more usual 

 expression in terms of the magnetic induction. It does, 

 however, show that, dynamically interpreted, the two different 

 forms of the expression are identical, and this covers the 

 whole field of observable physical activities, with the possible 

 exception of those associated with the phenomenon of 

 radiation. The exclusion of radiation is important, and 

 emphasises the essential difference between the two forms of 

 the theory, as well as the reason for the similarity in their 

 dynamical aspects. It appears, on general grounds, that the 

 purely radiation portions of the field, representing as they 

 do detached portions of the general dynamical system which 

 have become isolated from the remaining parts with a 

 definite quota of the total energy, will be completely 

 inoperative as regards the dynamical relations of the electrons 

 and of the aether in their immediate neighbourhood ; and 

 this view is supported by the known properties of such fields, 

 inasmuch as the energy in them, being equally divided 

 between the potential and kinetic types, is not represented 

 at all in the generalized Lagrangian function of the system. 

 Thus, from the point of view of the dynamics of the electron, 

 and this is all we are ultimately concerned with, we may 

 omit altogether the purely radiation portions of the field ; 



