CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
333 
These may be written 
A= - W +a T„ +1 (Aa)C, B= + XV +2 S„ +1 (Aa).C 
A= +X a b-“ +1 T*_ 1 (\b).D, B= — X a b-" +1 S„_ 1 (\b).D. 
Introducing a new constant St, we may therefore put 
C= St. b " +1 S„_ 1 (Ab) 
A= -mV +2 b-” +1 T, Tl (Aa)S B _ 1 (Xb) | 
B = +StA.~a" +3 b _ " +1 S, i+1 (Aa)S ;( _ 1 (Xb) j” 
D= — ^.a" +2 S« +1 (Aa) J 
(61) 
with the further equation, for the determination of A, 
S»+i(\a).T„_ 1 (\b) — T, i+1 (Xa).S /i _ 1 (Ab) = 0.(62) 
To construct this equation, I observe that 
„ /I d\ n sm x 
S„, = x n - 
may be written 
and that 
iX/ doG) 00 
■\r • i . n7r \ ■ tt . / . n + 1 
Xf' sm x-\- - +X 2 '* sm ( x -\~——tt 
T„, which =x u (~ s * n (2 JrX ), 
x 
may in like manner be written 
(Bn) 
Xf z sin ( x +) +X a * sin (x+~^n 
In fact 
(Bn) 
„ v „ 1 [n — l)n{n + l){n + 2) 1 , (n—3)(n — 2) . . . (?i + 3)(?i + 4) 1 
x --^i — 1 24 ‘„g"r ‘^4 
. 4 . 6.8 
■&c. 
1 
„„ V «_Kw + l) 1 (n-2){n-l) . . . (^ + 2)^+3) 1 , 
X '^ “ 2 * 2 . 4.6 ' • • 
F (B 1S ) 
J 
With this notation we may put 
