236 
MR. LUBBOCK’S RESEARCHES IN PHYSICAL ASTRONOMY'. 
a 
r 
a 3 , 
~ 2 a/ 3,0 
a°- , 
“ - 0‘i i 
2 a/ 2 3 ’ 
, + \ 
r 
La/ 
b - 3a< 
3,0 4 a l 
2 * 3 ,i jecos (»< + £ - 
- or) 
fa 3 
La/ 
*3,0 ’ 
5 
4 
a 2 ] 
— * 3,1 f esin (nt + e 
— ct) 
r 3 
L 2 
a 2 7 
— 6 
a/ 
3,0 
3a 3 ; 
2 a/ 3,1 
" S^ 3 ’ 2 . 
| e, cos ( n t + 
a 
r 
a 3 , 
~ 2 a/ “ 3, ° 
a- , 
WTi ^3.1 
Z a i 
+ l 
■>+“4 
a/ 
*3,0 — 
3 a°- , 
4 a/ 3 
'} ccos ("(' 
5 
-“-I: 
i,i) t + £ 
— 
4 
»,* ' 
) 
r 3 
L 2 
-,*., 
a, 2 - 
1,0 
3 a 3 , 
2 a/ 3,1 
• e t cos (nt + s 
The term b 3 2 e e t cos (z? — in the development of R gives 
d ex = — b 3 a e. cos (m — ) 
4 a/ ’ 
Jf /i=esinnr l = ecoszv 
d h = e cos ct d ct + sin nr d e 
de = “ &s,9«<«n («r - w,) 
h t — e t sin ct, 
a l n , 
= ~ b 3’* e i cos OT /= — 
Z ; = e t cos 
a 1 n 
® 8,2 h 
d Z = — e sin or d ct + cos m d e = - 
The integrals of which equations are 
h = iVsin (g t + C) 1= N cos (g t + C) 
h t = N t sin (g t + C) 1 = N, cos (g t + C) 
a J n , . a l n , 7 
~ o Sill *51 i Oo o /h 
4 a/ 3,2 ' ' 4 a/ 2 3,2 4 
N lS =-^ K ,* 
e cos (h t + e — ct) = N cos (n — g) t + e — C) 
which will agree with the previous solution, p. 233, if 
N = e,f, s — C = £ — ®r„ nk t = — g. 
This theory of the secular inequalities appears to require to be extended to 
the terms depending on higher powers of the eccentricities ; but I may remark 
that the coefficient of the term e 2 e ( 2 cos (2 ro- — 2 w ; ) in the development of R 
vanishes in the theory of the moon, or at least such part of it as is multiplied 
