IN PHYSICAL ASTRONOMY. 
55 
pend upon the secular inequalities of the constants s, ■&, & c., and the squares of 
the eccentricities. 
i = 1 + $ (»7 i >'“ - } - e { 1 + j {«7 *»•” - A I 4 *-' } } cos <“ ‘ + e - ”> 
" { 1 $ ~ 57 S)l ' + }«.«•(»' + ■—,) 
— r,cos (nt — n l t+ e — e,) — r 2 cos (2nt— 2nf, + 2 £— 2e ; ) — r 3 cos (3n<— 3 m/+ 3£ — 3s,) — &c. 
— {r 6 — r,} ecos (n t t + e t — ot) — {r 8 — rd ecos (2 n t — n t t + 2 £ — — w) 
— {r g — r 2 } e cos (3 w £ — 2 + 3 £ — 2 £, — sr) 
— {r 10 — r 3 }ecos (4 nt — 3 n t t + 4 e — 3 s, — ot) — {r n — r 4 } e cos (5 nt — 4n/ + 5 e — 4 s ( — to-) 
— {r 12 — r a } ecos (n< — 2n t t + s — 2s, + to-) — {r 13 — r 3 } ecos (2nt — 3n t t + 2e — 3e, + or) 
— {r It — r 4 }ecos (3 wf— 4w/+3s— 4g ( + rar) — r 16 e,cos (n ( f+e, — ra-,) — r 17 e,cos(n< + £— ra,) — &c. 
The constant part of jR 
= "*'{- if + 27* ( si " 5 -2 - + 47« 4 » C0S ^ - ”<> } See P- 29 - 
If this quantity = — F according to the notation of the Theor. Anal. vol. i. 
p. 336. 
d..(.-,ira?)4.-?f(|{)d. 
1 - e* /d F\ . 
dra=a?i ( — ) d t 
\de / 
/x e 
d g — d ra 
m. f 2 a- , 5 a 2 , , a 2 7 e, , 1 
dT 7 l v 3,0 “ T 5** 3 ’ 1 + 4^? 3 ’ 2 F cos OT ' } } 
Let, as hitherto, (Phil. Trans, for 1 830. p. 336.) 
= a { 1 — e' cos (0 — a) } 
h 2 v' 1 + s 2 
jx cos j 2 { V 1 + s 2 + e cos (a' — ra) 
Fig. 1. 
Fig. 2. 
