238 
MR. G. H. LIVENS ON THE 
wherein Cj is the true current density of electric flux ; 
T = 
477 ’ 
is the intensity of magnetic polarity, and 
Co = Ci + c Curl 1. 
It follows that 
Curl A 2 = E + 477 j" = E + Eo, 
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 (Jurl Ag is thus determined by the electric force in the held, 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 
».(b- i [,,,E]) 
an expression which agrees with that suggested by the relativity transformation. 
It must, however, be noted that the local term is necessary in the complete relation 
dehning-'the vector Ag for the simpler relation 
Curl A 2 = E, 
carries with it the consequence that 
div E = 0 
at all points of the held, 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 
- j(div I)BcZr+J' lBc-?/ 
^EcCml [1.J, EfE, 
dv 
+ j [ [ [Il-J E + E,,] dj. 
The second and fourth integrals transform by Green’s lemma to the volume 
integrals 
'(B (VI) + (IV) B) dv- I [[Curl [BJ E + E,;j+grad ([BJ E + E,) 
+ 
-([Ilh] div {E + E,)]dv, 
