144 
PHYSICS: II. BAT EM AN 
with the aid of the formulae 
E = rotB, H = 1 ^ + m 
c ot 
Let us now write 
M = H + iE = i rot L ^ - ^ + VA, 
c ot 
L = B - i A = — - + ic rot G, A = Q - i<$> = - c div G; 
Ot 
then in the case of an electric doublet we have 
G = i[p + i(vx P )]. 
To obtain the field of a magnetic doublet we write iq instead of p for the field of 
a magnetic pole of strength ju is derived from the magnetic potentials 
47T ^ 47T ^ 
If m = q — ip and 
G = - -fm + * (v X m)l = SM, say, 
V [_ C J V 
the derived field is that of an electric doublet and magnetic doublet which 
move together. When the vector g is given it is easy to determine the moment 
4-7rp of the electric doublet and the moment 4-7rq of the magnetic doublet. 
The function g(a)/v may be regarded as analogous to the fundamental 
potential function \ jr of electrostatics and Hertzian functions of higher order 
may be derived from it by differentiation just as potential functions involving 
spherical harmonics are derived from l/r by differentiation according to 
a method developed by Maxwell. 
Let us regard £, 77, f , g as functions of a and a parameter /3 then we obtain 
by differentiation a new Hertzian function whose x-component is 
It should be noticed that this expression for G x contains differentiation with 
regard to x, y and z but not t so that there is apparently a lack of symmetry. 
This is due to the fact that a is taken to be independent of (3; we can easily 
introduce a term involving a differentiation with regard to t by making use 
of the identity 
>>=*(?K(0 
but it is generally simpler and more convenient to retain the former expression. 
