426 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The imaginary part of this expression is iy = —- — ^J a i tt =z i h, 



V a TT 

 which is a true result. 



The real part is 

 — X — — ^— — V" — (1 — «) ( tan~i Va — ~) 



+ Va log ^^— ^ + Va log t^^ 



and 



, — X TT 



-[>.'^"(.„-VH-i) + lo.^]. 



Substituting this value of log tp in the expression for the quantity of 

 electricity on the conductor, 



from i = — I io t = P, ^ve obtain the final expression for that quantity 



(e) q — — -— % J a; + - -^^ ( tan-^ V« — - 1 + 1 — log ■ — ^ l 



When V = 1 this expression is the capacity of a strip of unit depth, from 

 the point Z> to a point P^ at a distance x towards the left; and we see 

 that there is a correction of amount 



to be added to x, to take into account the concentration of the electricity 

 at the corner. AVe may now calculate the amount of electricity on the 

 face D P, assuming the distribution to be uniform, only instead of x we 

 must use the value x + x^. 



