IN PHYSICAL ASTRONOMY. 
235 
i ^ j ~h ! ) ” / —— bn- -t — — bn - — bn • , j } cos A (re i — n t) + n t — zA 
+ { i(re _ Wj ) +w } Ufl/ 3 '*-! 2«3 3,. 4a,* 3, ,+ 1/ V' '' / 
/ (2 + i) a 2 7 (1 + 0 « 3 h L (8 + 9i) a* A 1 
n l X 16 a, 2 3,i “ 1 2 a 3 3,i 1 6 a, 2 3,t + 1 j 
2 ne 
{i{n - n,) + 2nj 
cos (n t — ur) cos (nt — n t t) +2 nt — 2 ^ 
+ sin (n t — zzz) sin (nt — n t t) + 2 n t — 2 zzr^ j. 
_ne f (3^— J) £! 6 — ( 3 * + II — b - , . j cos fi (n t — n, t) + n t - zA 
*(n-»,) l 8 a, 2 3*'- 1 8 a, 2 3,t+l/ ^ v • ) 
ne f 3 a 2 A ° 3 7 , /, \ 
_ W/ ) _ n } l4V 3 > l ~ 1 2 3 >* 4a^ 3 >*+ 1 J 
| cos (2 n t — 2 zzr) cos (nt — n t t) — nt + z?^ 
— sin (2 n t — 2 z?) sin ^z (ra t — ra, t) — w t + 
— — — cos (i (n t — n. t) + n t — zA — , n ° e ■ — cos (i (n t — n, t) + n t — zA 
4 (»-»,) a, V / ( ra ~ w /) a i V / 
(i (re 
nae 
— hi cos f i (n t — n. t) + nt — zA — ■ ae - ~ — cos (i (n t — n, t) + n t — zA 
a, da V / 2 i(n—n t ) 2 a, \ / 
(» ~ «,) 
ne, 
/ (3 + 9 i) 5 — b — ^ + 1) ^ 
{ i (?z — re,) + re + re, } \ 8 a, 2 ‘ /3 >* “ 1 a, W3 >* 8 a, 2 Ws >*+ 1 } 
| cos (nt — zzr) cos (re £ — n l t) + n t— -us + n t t — z?,^ 
— sin (n t — za) sin (nt — n t t) + n t — zz + re, £ — zz^j j 
f (3-3 i) a 2 , _ (1 -3i) a 2 1 
{ i (n — re,) — n + re, } 1 8 a, 2 3,i ~ 1 8 a, 2 ^ 3 >* + 1 J 
| cos (nt — zzr) cos (nt — n t t) — nt — zx + n t t — zzr,^ 
— sin (» i ■— zzr) sin (n t — re, t) — w t — zzr + t — |> 
It is easily seen that this expression is identical with that of p. 232, obtained 
by the direct integration of the differential equation of the second order. 
Considering the arguments 0 , n t e — z*, n t + s — sr,, still, however, neg- 
lecting for an instant the term 5 3 2 e e t cos (nr — sr ; ) which requires parti- 
cular attention, 
2 h 2 
