SIR G. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 57 



16. The S.F. of the P.F. W is L, so that the S.F. of P is ~; and in (2), 2, with 



otot 



/ 1 \ d iU _! 6 A cos 



--- __ 



da PQ~ MQ 2 'PQ' 



(2) - 2 A cos . th- *,- 2 ,A cos . 



AV cos 2 6 + Aa 2 cos 6 bd6 



7r - 

 AV + Aa 8 



_ 2 f 



MQ a PQ 



o 2 f MQ 2 -Aacose-CT 2 6 

 - ~ 2 ^ J MQ^ - PQ 



(4) 



is the S.F. of P, the rim potential of the circle AB, and L in (12), 8, is the S.F. of 

 the circular disc on AB. But then, from (8), L3, 12 ( I. /) is the solid angle of the 

 circle on the radius NP seen from Q on the circle on AB. 

 The S.F. of I, P.F. of the cylindrical skin, is then given by 



(5) J = f Qdb = 2^a \ 



J Ct/Ct J 



MQ 2 



fa 2 A* 6 



f rlf) 



= -rra (-2A 2 -6 2 -2Aa cos 0) ^r +47r6B 



J L Q 





(6) j 



2?r 



so that J is given in finite terms, while I is intractable, and requires to be given in a 

 series. And generally in these investigations we find the S.F. has the superiority 

 over the P.F. in simplicity of analytical structure. Thus the S.F. at P of the rod AB 

 is PA-PB, and of the electrified disc AB is y[AB 2 -(PA-PB) 2 ]. 



