SIR G. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 59 



and then -j should be J, the S.F. of the cylindrical skin, as a verification. Here 

 d(% 



(2) 



+ 



(3) 



*< 



b* \ d6 



ct 



( i , A!l v 8 



= J <- A > 



(5) N = |irPaA s +iTP-(a !1 +A a )-i7rQA(2a 3 +2A a -6 8 )-27rB6(a !! -A il ) 



f^ 



= T Pa (|A 2 + ^) -.^TrQA (2a 2 + 2A a -//) - T (a 2 - A 2 ) 6Q (MQ). 



In the interior of the solid cylinder of unit density, LAPLACE'S equation (2), G. 

 changes to 



AA . 



(6) -r-r A -y-r- + -jr- A -^y- + 4-TrA = 0, 



dA.\ dAJ db\ dbj 



or 



with V' = 



so that the S.F. N' is given by 



requiring the subtraction of 47r L 'A 2 in the interior volume. 



19. With these values of a P.F. and its S.F. the relations must verify in 

 6(1,2,3). 



Thus for the P.F. V and S.F. N of the solid cylinder, 



i dN_dv.. w 



" db ' 



implied in the integration in (l), 18, 



(2) _ ^ = 



db 



VOL. ocxx. A. K 



