PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
338 
(1.) For an external point, 
we observe that when t = 0, P = 2(P 
»+i 
U„ 
and that, always, P = e *** L2(F 
'\n +1 
U. 
)■ . i'i) 
where a' = ae 
The result, therefore, of an impulse on the sheet is such that initially the currents 
exert the same action on an external point, as a positive image of the magnetic system 
placed at the position of the electric image at the surface of the sheet. 
The points in which this imaginary magnetism is distributed then move towards the 
centre according to the law p' = pe~i™, while at the same time the intensity at each 
R' 
point increases according to the law P = Ie^a. 
When a=co we may take p — a and p — p' = ^-t, and P is constant; this result 
Z7T 
reproduces Maxwell’s expressions for a plane sheet. 
(2.) For a point on the other side of the shell 
where 
Rt r 
P=e - 4^2.CF( - 
\a 
Rt 
a"=ae + 27ra 
U,, 
(75) 
The effect is, therefore, the same as if the inducing magnetic system were reversed 
in sign, and the points in which it is distributed w^ere to move off to infinity in lines 
passing through the centre of the shell according to the law 
Rt 
p’—pe 2 ™, 
the intensity at each point diminishing according to the law 
. b< 
r=Ie-£i. 
§ 14. This result is so interesting that it may be well to give an independent demon¬ 
stration of it. Employing, as hitherto, spherical coordinates, let <t> be the current 
function for the currents in the sheet; P, the potential due to imaginary matter dis¬ 
tributed over it, with surface density $ ; the magnetic and vector potentials of the 
current system may be written 
