1888. ] and Kquipotential Curves. 193 
Further 
- {(Ologh jdlogh| _,  _, (oh /dh) 
_10G 1% 
Berea POU Ip, OF 
ick Sloe 
p, 0%  p, Ou 
ag ae 1/1 
=tan Oy 0” Po! Ps 
= _ 1 oF /1L of 
P, OY/ p, Ow 
oe Boe Bi 
Thus we obtain a new function of a complex variable, viz. 
zal ae nse, 
or, as we may write it, logh’—73’. Subtracting logh—7S we see 
that 
log 7 —1(9’—9$) 
or log de —itan™ \*. [| 
Y Po! Px 
is also expressible in the form of a function of a complex variable. 
The appearance of h in the latter of these two functions and that 
of S in the former, just preclude the possibility of using either of 
them for the purpose of modifying, so as to suit cases in which 
the boundaries are circular, the method adopted by Kirchhoff for 
discovering solutions in cases where the boundaries are straight. 
It is evident that the process we have employed could be 
repeated again and again, and thus we should be furnished with 
a whole series of expressions of a general form capable of being 
expressed as functions of a complex variable. These expressions, 
however, rapidly become more complicated. If we pursue the 
investigation one step further, we obtain an expression log h”— 73", 
where 
0/1 i Nee 0/1 NG 
680) aad BG) + 
"OE Po’ = PsP 2 OE P1 Ps J 
