236 MR. G. H. LIVENS ON THE 



of this quantity with the magnetism hides its true character, particularly as regards 

 its dependence on the velocity of the medium. 



Nevertheless many of the relations of the theory will be considerably simplified if 

 this procedure is adopted. 



12. The question of forces on fictitious magnetic poles moving in an electric field is 

 easily resolved by imparting to such poles a substantiality sufficient to allow us to talk 

 of forces on them, and then applying any of the general methods used in this theory. 

 The Lagrangian function of the system is still of the form 



L being that part of it which is not directly determined by the conditions in the field 

 and which will as usual be assumed to be a function of the positions and velocities 

 of the electric and magnetic elements only. The sequence of changes is then best 

 described by the fact that the action integral 



taken between fixed time limits is stationary subject to the implied conditions of the 

 field. If we assume generally that there are a number of discrete electric particles as 

 well in the field, these conditions may be written in the form 



div E-47rZe = 0, 

 div (B-H) + 47r2< = U, 



/( , TJ ^, 



Curl H --- - --- Zey, = 0, 



c at c 







wherein e is the charge of the typical electron and v t its velocity, m is the strength of 

 the typical magnetic particle whose velocity is v m and the sum 2 in each equation is 

 taken per unit volume at each place over the respective elements indicated in it. 



We now introduce four undetermined Lagrangian multiplying functions, two scalar 

 quantities fa and fa, and two vector quantities A, and A 2 , it is thus the variation of 



- \ 



dv B'-E' + ty, liv K + '2fa div (B-H) 



2 

 c dt I c \ dt dt 



c 



