MOTIONS IN A SPHERICAL CONDUCTOR. 
547 
Now j 2 /k 2 =Xp/iTrv 2 , and \= — Fp/47r= —p3~ j‘lirlx 1 , approximately. Hence (125) 
becomes 
2 02 
p 
1-j 
16(2w —l)7r 2 v 2 E 3 J ’ 
• (12C) 
In the second type we have 
FR 2 f„(&R) 
ItR^r'nQcll) + (/l+ l)-vp„(/cR) 
y 2 R 2 
n 
or 
xjj n (kl t)= — — ;Hty'»(Ht) 
(127), 
to the same degree of accuracy. For a first approximation k R=&, a root of xp„(3) = 0, 
and for a second 
m=M 1 
=3 
\ 
(128). 
By combining together in the proper way solutions of this type we should be able 
to represent analytically the decay of any given non-uniform electrification of the 
surface of the sphere. The formula (128) would indicate that in any particular mode 
the lines of flow of electricity in the sphere are for the most part closed curves, all 
those which abut on the surface being confined to a stratum of thickness p~3 2 /1 Gmr-v^Il. 
Forw=l, and ^/7 t= 1 , 4303, this = 1’42X 10“ 23 X/> 3 It -1 . In the case of any ordinary 
metallic conductor this would be much smaller than the dimensions of a molecule.* 
A result of this character cannot of course be interpreted literally. All that we can 
safely assert is that the currents by which the redistribution of the superficial 
electrification is effected are confined to a very thin film, and are probably subject to 
laws not yet investigated. 
In the case of a globe of water [p=7'18xl0 10 at 22° C.] the result is more 
intelligible ; viz., the thickness of the stratum in question is then= TSRr 1 . 
13. The case of periodic induced currents [A.=27rtp where p is prescribed] may be 
treated as follows. Let P, Q, It denote the components of electromotive force, viz. : 
Q=&c., K=&c, 
do: 
It is easily seen that if the suffix 0 be used to distinguish the parts of a, b, c, P, Q, 
R due to the inducing system, the functions %a 0 -j-?/b 0 -t-zc 0 and icP 0 -|-;>/Q 0 -}-zIt 0 must 
admit of expansion (in the neighbourhood of the origin) in the forms 
* There is nothing peculiar to Maxwell’s theory in the order of magnitude of this result. 
