of a Current running in a Cylindrical Coil, 205 



negative plate, A'C'B', as the approximate equivalent of the 

 given coil of wire. We shall now calculate the potential 



Fig. 1. 



• P 



V 

 ^^ 1° ^^ 



e 



C. i 



B 



produced at any point, P, by a uniform thin plate repre- 

 sented by AQB (fig. 2), the surface-density of attracting 

 matter on this plate being m. 



Fig. 2. 



Of course it is well known that this potential can be ex- 

 hibited by a series of Zonal Harmonics proceeding by powers, 



OP 



positive or negative, of the ratio — _, where is the centre 



of the plate and a its radius, according as P is near or 

 distant from it ; but when OP is not very much greater or 

 very much less than a, the series is inconvenient, owing to the 

 enormous number of terms that have to be taken to give a 

 good approximation. 



Hence we shall not use Spherical Harmonics. 



