PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
293 
Remembering that the surface has a constant over it, we have as the surface con¬ 
dition (Professor C. Niven, ‘Phil. Trans./ 1881, p. 313) 
it _ o 
A 3a ' 
the normal outwards being in the direction of a increasing: and (from the same 
source) within the conductor 
V 2 i/f = 0. 
Hence drp/dn being known, xjj is uniquely determined (Maxwell, vol. 5, § 100, e ). 
Let us write xp = d^/di, and 
F = F + 
Ada 
then our equations are typified by 
G = G +H 
H = H + c%’ 
dF 
au ~ d t 
BCa = | (CH-) - I (BG-) y 
dc 
4ttmBC = |(Cy) -|(B/3) j 
If now the conductor be such that no external field can give rise to currents 
normal to a surfaces, then for all values of F, G', H' consistent with 
at the surface, and 
F = 0 
dt 
4 (BCF) +1 (CAG') + | (ABH') = 0 
da 
dc 
within the conductor, u must everywhere vanish; that is, inside, 
dF' -| 
0 = 
d t 
0 = | (Cy) - ? m 
Now F' is everywhere zero before the external field is brought into existence, 
hence by the former equation (1) it is everywhere zero permanently. 
