G2 
SIR a. GREENHILL ON ELECTROMAGNETIC INTEGRALS. 
To reduce to this standard form, put 
(3) 2av^(A^ + //)+2Aa cos 0 = — 
2av/( A^ + 6")+2Aa = — 2a^/(A' + />^) — 2Aa = — 
y-Ui . 
h Ti — t \/T 
(4) 
and to reduce put 
(5) 2a^/+ V) —2Aa cos 0 = — 
2av^(A^ + ?>^) — 2Aa = 2«y/(A^+6^) +2Aa = 7n^{t.2 — T2) 
a^ + A^ + h'^ + 2a^/{A^ + b'^) — [a +a/(A^ + //)]^ = tj), 
— Ua dt 
( 6 ) 
Q, = 
■Tg 
v/T 
Then the sequence runs 
(7) 00 > > /‘g > ^ > ^3> T2> - 00, 
and we take 
/o^ -fnr _ r'\/(h t?) dr _ , -1 /ii Tj P, 1-1 t /— dn-’ t ^ 
- J„ y-u 'VG-;i:7;-“‘ VT:=T.r 'v ^ 
= dn“^ \/^~ — 
/.G' = J1 ^^ 0 .^ = 
tz — T2 
t\ — r2 
(10) Qj = 7 i^i + 2G zn/’^G', Qj = 7r/i + 2G zs^gG^ 
and with Z^-/ = 2/ 
(11) ^}(PZ) = 27r/+2Gzn2/G' + 2Gy'sn2/G' 
= 1} (MQ) = 2?!— Q. 
Interpreted geometrically on fig. 2, with 
( 12 ) 
(13) 
(14) 
(15) 
sn/.G' = 
^ ^2 '^’2 
.n (1 -/,) G' =vzt V:-Z:= 
-/=cr = VZ7, = ;^r7(i^. 
^2 —T2 
h 
_ \/(A^+5^) — A _ gn (1 _ /■) Q.' 
v/(A^ + /P)+A“ h -ysnG Z)G. 
