538 
PROFESSOR H. LAMB OR ELECTRICAL 
The first derivatives of F, G, H are, however, discontinuous, viz., if dv, dv" be 
elements of the normal drawn inwards and outwards respectively, we must have 
dF dF 
dv'+dv” 
= — 47 Til' 
da da_ 
dv l+ dv"~ 
— inv' 
dB. cm _ 
dv' + dv"~ 
— 47 TlV 
('?)> 
which equations now replace (1). Hence, and from (74) we deduce 
-»! X „+«X„-(«+l)X_„_ 1 =^ x ».(78), 
P 
when r=R, the radius of the shell. 
In free motion X ?J =0, and thence 
x _i 4ttR /* nX 
T =- x . ( ' 9) - 
In the case of currents induced by a system external to the shell, we find 
*»=IT^ X '.< 80) ’ 
and 
x —i=-]vh x .< 81 >- 
when r has the value (79). The value of X ;t can be found as before when the nature 
of the inducing system is known. Writing \=2 ?rip we see from (80) that if the 
period of the disturbance be small compared with r the shell will almost completely 
shelter the enclosed region from the electromagnetic action of the external system. 
The case where the inducing system is inside the shell may be treated in a similar 
manner. We have to introduce a function X-«-i i°r the internal space, whilst X„ is 
zero. 
7. When the magnetic permeability /x of the substance of the conductor differs 
sensibly from unity, the processes of the foregoing articles require some modification. 
The equations (1) must then be replaced by 
V 3 F = — 47 TjlV " 
V 3 G = — 47 t/jlv > 
V 3 H = — 47 TfJLW _ 
(82), 
* See Lord Rayleigh, Phil. Mag., May, 1882, p. 344. 
