IN PHYSICAL ASTRONOMY. 
235 
- ( £ + _ £) .”-/_iL_ A . -) —— l . — J*iL 5 i cos (i (n t — n t) + n t — w \ 
+ {i +n} UV 3 ’*- 1 2a/ 3,, 4a ( 23 >’+*/ [ ) 
2ne f _ (2 + Q a 2 A 0 + 0 <* 3 a , (8 + 9i) a 2 „ 1 
{«(»-»,) + 2m} L 16 a, 2 3)1-1 2 a , 3 3,i 16 3,j +1 j 
^ cos (nt — zx) cos (n t — n, t) -\-2nt — 2 zx^j 
+ sin (n t — et) sin (nt — n,t) + 2 n t — 2 zx^j j> 
+ IJ^j { ^TT 22 $ hi -. - <12 r 22 ff hi +i} “ s 0 (»<-»,») + «<- ®) 
ne /3a 2 . a 3 . fl 2 /. 1 
~ {»(»-«,) - n} 14 a,® 3 '* ~ 1 2^ 3 ’* 4a ( 2 3 >*+ 1 J 
| cos (2 m t — 2 ra-) cos (n t — n, t) — n t + zx^ 
— sin (2 n t — 2 ct) sin («t — n, 0 — w t ^ 
-wae-id cos (i (n t — n. t) + ra t — bA — ^ - 1 - 0 - -id cos (i (nt — n,t) + nt — raA 
4(71-71,) a, V / (»-»/) a i\ / 
-a_Me-M cos ({(nt — n,t) + nt — zx\ —‘ O’ n — cos A(m £ — n, t) + n t — bA 
(n-n,)a,da \ / 2i(n-n^a, \ / 
_ 71 e i _ / (3 + 9 i) a 2 , _ia, _ (1+0 a 2 , 1 
{ i (w — «,) + n + n, } l 8 af 3,1-1 a, 3)1 8 a/ 2 3,8 + 1 J 
| cos (nt — zx) cos (m £ — n, t) + 
— sin (n t — zx) sin (n t — n, t) + n t — -us + n, t — zx,^ j 
__ _»£i_ f (3 - 3 Q a 2 6 _ (1 — 3 i) a^ 1 
{i (ra — n,) — n + n,} 1 8 a, 2 3,i—l g a ^63,i + lj 
| cos (nt — zx) cos ^i(nt — n,t) — nt — zx + n,t — zx,^J 
— sin (n t — zx) sin (i(nt — n,t) — nt — zx + n,t — zx,^ j> 
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, nt — zx, nt + s — zs,, still, however, neg¬ 
lecting for an instant the term -~ 2 b 3 i e e, cos (ra- — zz,) which requires parti- 
cular attention, 
2 h 2 
