FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
471 
via 
4 w/tj} -3 
+ 
/ 
(199) 
because is the tensor of the magnetic force due to m in the medium when 
of infinite extent. Therefore 
a = ;<1 ~ fe- . .(200) 
/“l + /L 
The magnetic potential fl, such that R = — VH is the polar force in either region, is 
therefore the potential of at A and of cr over the interface. 
But if we put matter n at the image B, of amount 
n = K 
/ l i + H 
m 
p r 
the normal component of R 1 on the [jl 1 side due to n and the pole m will be 
( 201 ) 
ma 
na 
47r / u 1 r 3 4 ttt 3 
ma j 
49r/r 1 r 8 2 ’ 
( 202 ) 
the same value as before; the force R x on the side is, therefore, the same as that 
due to matter m/^ at A and matter n at B; whilst on the /x 2 side the force R 2 is 
2??z 
that due to matter m/u, T at A and matter also at A, that is, to matter-at A. 
Pi + P» 
Thus in the /x 3 medium the force R 2 is radial from A as if there were no change of 
inductivity, though altered in intensity. 
The repulsion between the pole m and the solid mass is not the repulsion between 
the matters w/p. 1 and n of the potential, but is 
= m x magnetic force at A due to matter n at B, 
= n X magnetic force at B due to matter m/A at A, 
mn _/<] — fin to 2 
4-n- (2a) 2 + fi 2 4^/^ (2a) 2 ’ 
(203) 
becoming an attraction when > /r l5 making n negative. When /x 2 = 0, the 
repulsion is 
W? 
477 -yUj (2a-) 2 ’ 
when /x 2 — oo, it is turned into an attraction of equal amount. 
Similarly, if we consider the attraction to be the resultant force between m and the 
interfacial matter cr, we shall get the same result by 
4wr 3 
(204) 
the quantity summed (over the interface) being cr X normal component of magnetic 
