SIR G. GREENHlLL ON ELECTROMAGNETIC INTEGRALS. 
.51 
12 . By logarithmic clifFerentiation of ( 6 ), § lU, 
( 1 ) 
ds 
dr^ 
s — So r,—. r — n r 
and with s — Sg, s^, for = + r.j't's, 
(2) 
( 3 ) 
( 4 ) 
( 5 ) 
Si—s + s.,—s 
O' —S3 
2ar 
cr — So 
r -r^} \ 
2ar 
y(si-s. Sa-s) _ r^-rjri 
O' —So 
V 
s-s^ _ s/{ri-r^. r^-r./) 
<T — So 
2ar 
(o- —Sa)’^ 4a 
( 6 ) 
ds / 4 2 2\ — 2 dr 
- = (■/’ - >’2 ) , o 3 
O' —So 4 a 7”* 
( 7 ) 
vf(o-—S 3 ) ds _ _ — 2 a dr 
\/S x/{r'f-r\r‘'-r.f) 
Then with 
( 8 ) 6 = 2 sin ^ a / = 2 cos ^ a/ ^ , dO = 
V V 7V-'>V 
— 27’ dr 
v/(7^/-7•^7■"-7•/)’ 
( 9 ) 
dP = 
ado _ —2adr _s/{<T—s-^ds 
W ” x/{ri-r\r^-ri) ~ 7® 
^ d^eK = dn/K'd 2 eK = 
T Si S3 
EB 
PB 
cZ2cK. 
Comparing this with the previous form in (4), § 3, 
(10) 
T-T-. 2 a d(jo oAl.13 7 7 ^ 
dP = — — = _ deG, 
7-3 Aw AP 
( 11 ) 
EB _ AB p 
PB AP 
2 K ^ AB ■ PB 2y' 
G EB'AP l-,c 
( 12 ) 
VOL. COXX.-A. 
(l-^)K - Gy', KP = G7y'. 
I 
