IN PHYSICAL ASTRONOMY. 
345 
+ % sin (M*+2n,f— w,)— ee J c g °® (2 n,t ^ c ?* (2w*+2«*—w--®r,)4-&c. 
rr i sin ft+\- 2 »} = aa l | (l - L ^ l ) (nt+n,t- 2v) 
~ 4- e ^ («,*+*- 2 *) + g °* ( 2 w^+^-ar- 2 v) 
+ T e2 sin (3nt+n l t—2nf—2p) + g °® {nt—nj— 2*+2v) 
~ Y e / sin («<+»■ -2v) + f e e, g °® (*4-*, -2*) 
~ T ee ‘ sin (2w<— ®r+®,-2v) + -|shi (^+2w/-^-2v) 
— X ee / sin P w /+» f — ^/— 2v) + ^ (2n/4-2w/— w— or, — 2»)+&c. 
f e 3 / 3 \ e 2 / Qe~\ 
r = a < 1 + -7^- — e v 1 — “s' e2 y cos ( nt ~ m ) — 77 ( 1 — -g- ) cos (2/^—2^) 
3 e 4 
g- e 3 cos (3nt—3&) g- cos (4ra£— 4 to-) + &c. 
r 3 e 2 / e 2 \ e 2 ( e 2 \ 
r 2 = a 2 jl+~o 2e^l s~) cos { nt — rs ) — ^1 — — jcos ( 2nt — 2vr ) 
— — cos (3nt—3zo) — -g- cos {Ant— 4z?) + & c. 
r = a 3 1 1 4 "2 e2 ^ e (l ^ c 2 ) cos ( w ^ — w ) 
9 / e 2 \ 53 
+ 77 e 2 ^1 — ^g) cos 2nt—2zs 4- ~g~ e 3 cos (3w£— 3w) 
31 
4 - -j- e 4 cos (4w£— 4sr) 4 - &c. 
r 2« a - 
If the coefficient of cos n 0 in the development of < 1 — — cos 6 4- j 
according to cosines of arcs mulitples of 6 is called b 2m 
