Development 
of R accord- 
ing to powers 
of 
38 MR. LUBBOCK’S RESEARCHES 
+ *i { T - “ ^5 } e f cos ( 2 »/* + 2 e, - 2 or,) 
— ef cos (n < + n/ + £ + s y — 2 ra- ) 
o4 fl, 
— mi A fL e 2 cos (3 n < — + 3 £ — £, — 2 cr.) 
64 a t * 
— ??! / AA -fL e, 2 cos (n t — 3 w / < + £ — 3 £ y -f 2 ra-,) 
— »n / A iL e< 2 cos (2nt-4n j < + 2 £ — 4 £, + 2 ar ( ) 
— »», -L-^ e, 2 cos (3«t — 5» y < + 3£ — 5f, + 2 or,) 
[5/J 
[58] 
[60] 
[63] 
[64] 
[65] 
9 Qp • l 
— m t — sin 2 — cos (n t -f- n i t -j- e + £, — 2 v) 
4 a 
— j?i A fL sin 2 -L- cos (2 n t + 2 £ — 2 v) 
2 a, 3 2 v ' 
— mi 4- ^sin 2 -i- cos (2 n, t + 2 £, — 2 r) 
Z Uf z 
— m, A fL sin 2 -L- cos (3 n t — w ; t + 3 £ — £, — 2 v) 
8 af 2 
— m j [r —* sin 5 -f- c os (w t — 3n, t + e — 3 e, + 2-v) 
8 o' 2 
[75] 
[76] 
[77] 
[78] 
[79] 
If according to the notation of M. Damoiseau, (Th6orie Lunaire, p. 547, Me- 
I 
moires des Savans Etrangers,) n t — n t t + e — s, — t, and x and a be put for the 
mean anomalies of m and m l respectively and y for the distance of the planet 
m from its node, or, what is the same in the Lunar Theory, the distance of the 
moon from her node reckoned on the ecliptic (/, = 0), 
[0] 
+ ( ( cos 2 A - (* +tf }\ ± - ft .A + -I + Sin 2 * ±(l+E 
l\ 2 2 / af af\ 8 a?) 2 a, 2 V 8 a?) 
+ 
(e 1 + e, 2 ) n 
n /. 3 a l \ 1 . , f 3 a 2 , 3 
af V 2 af) / T I 4 fl, s T 2 
11 
8i “ ! Ta7 + f + 
cos 2 l 
[2] 
