102 A NEW METHOD OF DETERMINING 
and 
SY (e ) Bef da = Sie sin tg +8 9 — Beg: 
But since 
m= 1 + ge — (2e— fe’ + sige?) cos g — (he — ge! + aige*) cos 2g 
a? 
— (4é — e’) cos 3g — ete. 
we have 
Hence the integral just given is simply ae sin kg. 
A and B can then be written 
1 a(1—e’) —r? Q2psinw dR) , 
A=—3 al (26 oso 3e ) 5 — 
eas - +P Te aoe ie oe kg | 
2 psi dR) 
a p OF, hoe Fh Attlee 9 | 
B= 5 [ (22 cosa + 8¢) Sk R sin kg ofle\ cos kg e 
Putting 
2 
{= > R™ cos x y, 
we have likewise 
Oe = Te a oe 2° sino = v 1a Ss 2 RO Sinz 
—COS @ Les — aR aR cos XV 5 7 oo = edy —e — 7 Y: 
Introducing these values of 2 ” cos o, and 2° sin @ into the expressions for A and 
BL, after integration relative to y we can write W in the form 
VSS oo ae) (xy 4+ Bt ) ; 
