238 MR. G. H. LIVENS ON THE 



wherein C, is the true current density of electric flux ; 



B-H 



47T 



is the intensity of magnetic polarity, and 



C EE^ + c Curl I. 

 It follows that 



Curl A 2 = E + 47r C dt = E + E , 



say. The vector A 2 is a slightly more general form of the second vector potential 

 introduced in our previous dynamical discussion and its curl is identical with the curl 

 of that vector. 



The main part of Curl A 2 is thus determined by the electric force in the field, and 

 its mechanically effective part is completely represented by this vector ; the forcive on 

 the moving magnetic pole is thus to all intents and purposes equal to 



an expression which agrees with that suggested by the relativity transformation. 



It must, however, he noted that the local term is necessary in the complete relation 

 defining the vector A 2 for the simpler relation 



Curl A 2 = E, 



carries with it the consequence that 



div E = 



at all points of the field, and this is true only of those points where there is no 

 electricity. 



The expression for the forcive on the magnetic media is now attainable by regarding 

 it as the resultant of the forces on its contained poles ; for the volume v bounded by 

 the closed surface/, it is in fact 



Curl Il ''' E + E dv 



The second and fourth integrals transform by GREEN'S lemma to the volume 

 integrals 



J(B (VI) + (IV) B) dv- J[[Curl [LJ E + EJ+grad ([I,J E + E ) 



