SIR G. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 
59 
and then 
dN 
da 
should be J, the S.F. of 
the cylindrical skin, as 
a verification. 
(2) 
j PQ dh = 
pA^+«' + // 2QA, 
a 
(3) 
1 PQ cos h do 
-|PA 
a 
(4) 
= |(«-At(l+4) 
do 
PQ 
-(rd AQ(P^' "''+4B6), 
a 
(5) N = |7rP«A- + i7rP-(a^ + A^)-.^7rQA(2rr + 2A^-6^)-27rB6(ffi^-A^) 
ct 
= TrPa (t A^+//) -^ttQA (2r^^ + 2A^-6^0 -tt 60 (MQ). 
In the interior of the solid cylinder of unit density, Laplace’s equation (2), § 6, 
changes to 
( 6 ) 
or with V' = V + -n-A?, 
d i A dV'\ , d / , dV'\ 
d i \ dY\ , d / A dV\ , . ^ 
so that the S.F. is given by 
( 8 ) 
dW ^ .dY' , , dY 
= 27 rA = 27 rA -rr > 
dA 
db 
dh 
dW ^ . dY' .A fdY 
=- 27 rA^ =- 27 rA Ai+ 27 rA 
dh dA \dA 
dY 
= -2xA^-47r“Ah 
dA 
requiring the subtraction of 47r“A^ 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, 
( 1 ) 
1 dN dV 
27rA dA dh 
implied in the integration in (1), § 18, 
dN 
= W. 
( 2 ) 
=-2xAf^ = L. 
dh dA 
VOL. CCXX.-A. 
K 
