CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
343 
we 
have 
— K 2 {JL~ = i. 
. Attvico 
■ ( 11 ) 
/ , . 47 rmco . . N 
• — i -=±(i> —«i) suppose. 
We must take only the positive sign since 11 = 0 when z= — co . 
Thus 
p_ e wj OT ( K p)( — Ae^+Be^-) within the solid : 
outside 
P=e^J»(K / t>).Ce-« 
and the conditions of continuity give us 
— A + B = C, —kA+//.B =— kC, 
whence 
B=—.A, C=^.A 
/C + yU- /C + yU, 
( 12 ) 
Let us confine our attention now to the value of C which expresses the action of 
the sheet on external points 
k — p + A 
C=A.- 
k Ar'p — qi 
= A (jp'+q'i). 
similarly, corresponding to the term A'e we find 
C'=k'{p-q'.i). 
Let 
Ae^d- A'e - "" <?> =^1 cos sin m( f> 
Ce^+C'e-^=© cos m<£+13 sin m<f) 
®=c+c'=a/+w 1 
33=(C-C')i=3Sp'-as'J ' 
Let 
then corresponding to a term in 
P 0 = (SI cos sin m</))e K *J M (/cp), 
there exists in P (outside) the term 
[SIM' cos (9w<£+d') + 33 M' s in (m<£+&')]e ' C -J,»(«/>) .... (14) 
