THEORY OF ELECTROMAGNETISM. 
701 
4ir H VZ = B.(17), 
SVB = 0, [SdXB] a+4 =0.(18), 
and B is called the magnetic induction. 
These are proved by previously proving that 
B = WA.(19), 
where A is a vector which satisfies the condition 
{Yd%A] a + 6 =0 .(20). 
A is assumed to be an intensity, and B a flux, so that (§ 8 above), 
SV'B' = 0 , [8cfc'B']. + 4 =0.(21), 
B' = VV'A' , [VdZA'] a + b = 0.(22). 
This relation between B and H is not the usually accepted one, but it is certainly 
true on the present theory. It will appear later on that the value thus arrived at 
of B , the magnetic induction at the point p , is independent of the particular position 
which is chosen as a standard of reference. 
In the present theory I—assumed a flux—called the magnetic moment per unit 
volume is defined by the equation 
B'-H' = 4771'.(23), 
from which it does not follow that B — H = ini, since B and I are fluxes and H is 
an intensity. It does follow, however, that 
B" - H" = 4nl" .(24). 
27. The equations of last article, it will be observed, do not represent fundamental 
assumptions. They are given here merely to indicate how the familiar symbols 
involved appear in the present theory. We now return to the fundamental 
assumptions. 
The independent* variables, of which l is supposed a given explicit function, are 
6, 0 ; p, p', V; d, D, C, H.. (25) ; 
x is supposed a given explicit function of 
0, 0 ; ¥, K, H.(26). 
* See § 31 below. 
