SIR G. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 
49 
Produce PE on fig. 2 to meet Ox in G, and describe the sphere, centre G, 
passing througli the circle on AB. Then P, E are inverse points in this 
sphere, and 
(15) 
(16) 
PQ _ PA _ PB _ PA + PB _ 
EQ EA EB AB 2 a ’ 
2eK = ^ ^ 
Sa —5;, (T —53 -So —^3 2A / 
(17) 
sn 2 eK = 
O + r., 
2 PQ 
sin 0 = 
a sin 0 
~w~ 
sin <p, 
(p = am 2 cK, 
where 0 = AEQ on fig. 1 , and 
(18) 
OE ^ OB ^ BE 
OB OD BD' 
And with ODQ — cp' — OQE on fig. I, 
(19) 
Sill (p' ~ K Sin (f). 
cos cp' — Af/) = dn 2 eK, 
so that Qq = AB cos (p' — AB dn 2 cK. 
On fig. 2 , and from ( 7 ), (I4), 
( 20 ) 
2a ^ EB ^ hp 
r. + r, PB BD’ 
and with DE^ = DPB = \/a, 
(21) Bp^ = BD^cos^ V. + BE^sinG/. = BD^ /c'), 
(22) A a, k') = dn/K', V- = am/K', 
and 
DEP = DpB = am (1 -/) K'. 
