SIR G. GKEENHILL ON ELECTROMAGNETIC INTEGRALS. 49 



Produce PE on fig. 2 to meet Ox in G, and describe the sphere, centre G, 

 passing through the circle on AB. Then P, E are inverse points in this 

 sphere, and 



(i *\ 



EQ EA " EB AB 2a 



(16) sn 2 2eK = ^ = ^ . ^ = ^ 



8 



2A / ' 



/ * H \ ,- TT' ?** i ?*> /\ 05 S1H V * r T7" 



(17) sn 2eK = ~ sin W : -^7=\ = sin <j>, <f> = am 2eJV, 



where ^ = AEQ on fig. 1, and 



, , _ OE _ OB BE 



= OB ~ OD " = BD ' 



And with ODQ = </>' = OQE on fig. 1 , 

 (19) sin </>' = K sin <-/>, cos ^' = A</> = dn 2cK, 



so that Qg = AB cos <^ AB dn 2eK. 

 On fig. 2, and from (7), (14), 



/on\ j n^/ " x i EB 



dll/K 



and with DEp - DPB = V', 



(21) Bp 2 = BD'cos^ + BE'siu 2 ^ = BD a A 2 (^, K'), 



(22) A (Vr, *') = dn/K', V = am/K', 



and 



DEP = DpB = am (1 -/) K'. 



