160] 



CONFORM AL REPRESENTATION. 



321 



As we have interchanged z and w since equation (13) we must 

 interchange x, y with u, v throughout, so that instead of (7) we 

 use, putting a 2 6 2 = 1, 



x = log (Va 2 + X + V^ + X-l}. 



Fm. 66 &. UT-plane. 



Now choosing for the functions V and ^, Vx y 



, we 



obtain on the cylinders whose semi-axes are a x = x/a 2 + \ and 

 a 2 = x/a 2 + X 2 the whole charge e = \, with the potentials 



The capacity of the pair of cylinders is accordingly 



1 



2 log 



By interchanging the functions V and M* we may find the dis- 

 tribution on the hyperbolic cylinders, and in particular by putting 

 y = 0, y 7T/2 we may find the distribution on the edge of an in- 

 finite plate in presence of a second infinite plate at right angles 

 with it beyond the edge. 



W. E. 21 



