CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
347 
Equation (20) now becomes 
the same characteristic equation as in § 10. 
We may now show that these results verify the second of (19) as the reader may 
easily convince himself by substitution. 
(a.) When the inducing magnetism or currents are outside the shell altogether, 
P 0 will consist of a series of terms of the form 
(23) 
and for the value of P we shall have 
S- • (24) 
and where 
(25) 
a 
we shall put as before 
x=\r, a=A.a, {3=\ b, S„(«) = S, S rt ( / d) = S < „ . . 
When r— a, 
and when r— b, 
By the help of the formulae of reduction in § 10, we can put the result of the calcula¬ 
tion of the new coefficients B l5 B. : , C, D into somewhat elegant forms. 
MDCCCLXXX I. 
2 z 
