of a Current running in a Cylindrical Coil. 211 



and we find -j- of the right-hand side of (16) equal to 



—A e -\-k'K sin ; so that if 12 is the conical angle subtended 

 at P by the circle, or the magnetic potential per unit current 

 in the circle, we have the very simple expression 



n = 2A,-2fc / Ksin0 (18) 



Again, supposing that the depth, 00' (fig. 1), of a coil con- 

 sisting of a single series of circular currents is small com- 

 pared with the distance of the point P from any part of it, 

 the two terminal plates, AOB, A'C'B' may be considered as 

 close together, and the potential of the coil at P is the value 

 of V in (16) minus the value obtained by putting z + h for z, 

 where h = 00'. Hence the potential in such a case is — mhtl, 

 i. e., at any point in space whose distance from every part of a 

 coil is great compared with the depth of the coil, the potential is 



2roA(A,-#Ksin0) (19) 



The modulus k which appears in these equations, being 



(-#•' 



is constant at all points for which — is constant : 



P 



i. e., at all points on any circle which cuts that described on 

 AB as diameter orthogonally. The circles which cut this 



Fig. 3. 



latter orthogonally, having their centres on AB, are most 

 readily drawn by joining A to points, m, n, p, . , . (fig. 3) on 



