318 MR. S. H. BURBURY ON THE INDUCTION OF ELECTRIC 



and A. is the positive root of 



y 8 , * , . 



8 ~ r ~ 



and therefore on the sheet 



Now, x ' ia the function which satisfies d-^Jdv = ?F + wG = (Aj A 2 ) 

 on S, and V 2 ^ within S. 



That is, x = Gary, when C = (Aj A 2 )/(a 2 + Zr), and this is independent of z. We 

 can therefore make the shell self-inductive. 



Again, on the sheet 



- -- , = 477-U ; 

 dv dv 



that is, 



d& 

 and, therefore, 



Aj = A . 4irab*c ~ . 

 Similarly, 



A 2 = A . 47ra 3 6c ~ . 



We have then to satisfy the equations 



,dq<>y 



TT . . 



r U s= - A -5 = K A 47ra& 8 c 

 A A fc 2 



or 



If we now make a-jh = If (piss), where p is constant, we have, by differentiation, 



A 



which determines K in terms of (1) a, 6, c, (2) the absolute thickness of the shell, 

 (3) tr, the specific resistance of the material of which the shell is composed. It is 

 independent of the absolute value of the current function. 



