IN PHYSICAL ASTRONOMY. 
59 
//t-y 
m, n- 
,Ki e i cos («,* + £, — «•,) 
p (n — 77 , ) (n + 77,) 2 a, 
m , tt 2 | 4 n f 3 a* b a_ _ _a®_ b T 
jiT (ti — 77,) (3 77 — 77,) [ (2 77 — 77 ,) 1 4 a, 2 3,1 2a ( 3,2 4 a, 2 3,3 / 
9 a 2 , ,2a, a 2 , ] , 0 , . , 0 . 
- T ^ 63 ’ 1 + ~a bs ’° ~ 4 m * 3,3 P C ° S ( 2 ~ n,t + 2 £ ” £/ “ ^ 
77i y 7i 2 [ 6 77 /3a 2 , a , a 2 , \ 
/T (2 77 — 77,) (4 77 - 2 n,) j (3 77 - 2 77 ,) \ 4m* 3 ’ 2 2^ 3,3 ~4m* 3>4 J 
- ^^3,2 + — Ks - —K* U, COS (3 77 * - 2 77,* + 3 £ - 2 £, - W, ) 
flj flj m CL ^ J 
m, 77 3 J" 877 /3a 2 , a, a 5 ^ 1 
//, (3 77 — 2 77,) (5 n — 3 77 y ) \ (4 77 — 3 77 ,) 14 a* 3,3 2 a, 3,4 4a, 23,s J 
a 2 1 
— 6 3 5 > e, cos (4 77 < — 3 ?7,£ + 4 s — 3 £, — or,) 
«<“ ’ J 
15a 2 , ,4a, 3 1 
T — i 6 3,3 + — 0 3) 4 
[15] 
[17] 
[18] 
4 a, 2 
a, 4? a. 
[19] 
777 , 7i 2 j" 2 77 /2 a 2 a 2 , _ a , 3a s , 1 
ju, 2 77, (2 77 — 2 77,) 1 (n — 2 ?7 y ) L a ( 2 2 a, 2 3,0 2 a, 3,1 4 a, 2 3,2 J 
2 fl' ^2 | 
+ — r + — 2 &3,0 — — ®3,1 f C0S (77 t — 2 77,* + £ — £, + OT,) 
a,- a, a, J 
f 4 77 / a 2 ^ a f. . 3 a 2 ^ / 
fT (77 - 3 77,) (3 77 — 3 77,) / (2 77 — 3 77,) j. ~ 4o* h ' ~ 2 m, 3, ~ + 4aj* 3,3 J 
+ TTa fc 3*i ~^^ 3 - 2 + t/T^ 3 ’ 3 } 6 ' 008 (2 77 f — 3 77/ + 2£ — 3 £, + ®,) 
_ 777, 
4 a, 2 ' 
[h (2 77 — 4 77,) (4 77 — 4 77,) 1 (3 77 
6 77 / a 2 £ a , 3 a 2 ^ / 
; - 4 77,) L — 4a; 2 3,2 ~ 2a, 3,3 + To/ 2 ” 3 ’ 4 J 
+ ^ 3j2 — — 6 3 ,s +|^ 6 3,4 }-e ( cos (3?7* — 477,i + 3£ — 4 s, + w,) 
dy Cl y Zi (1 y 
77 2 
J 877 f _ a 2 ^ (L £ I 3 a 2 ^ 1 
ja- (3 77 — 5 77,) (5 ?7 — 5 77 ,) | (4 a — 5 ?7,) l 4 a, 2 3,3 2 a, 3,4 4 a, 2 3,5 J 
+ S^„_i? S) , 4+ 3 ^S JiS |c,cos(4»t- 5n,l+ 4s — 5>, + ar,) 
[ 20 ] 
[ 21 ] 
[ 22 ] 
[23] 
Substituting in the equations of p. 45, for R* their values and neglecting 
e 2 , ee,, e 2 , and sin 2 [ , 
i 2 
Expression 
for the reci- 
procal of the 
radius vector, 
when a <C a,. 
