IN PHYSICAL ASTRONOMY. 
5 
+ {r 5 r, + 2 r 0 r 7 } e,cos (2 < + z) + {r „ 2 + r 4 r 3 + r,r y + r, r 10 }e 2 cos 2 x 
[7] [ 8 ] 
+ r 3 + 2 r 0 r 9 } e 2 cos (2 t — 2 x) + (r 4 r 2 + 2 r 0 r 10 }e 2 cos (2 < + 2 .r) 
[9] [ 10 ] 
+ { r i J ‘i 3 + r i r it + r 2 r 5 + r 6 r± + r 3 r 7 + 2 r 0 r n } ee t cos (x + z) 
[U] 
+ {r n r i + r*r 6 + r 5 r 3 + 2 r 0 r,J ee l cos (2 t — x — z) 
[ 12 ] 
+ {*•, 1 ^ + r 2 r 7 + r 3 r 4 + 2 r 0 r 13 } ee, cos (2 < + x + 2 ) 
[13] 
+ {r^r, + r lb r { + r 2 r 5 + r 6 r 3 + r 7 r 4 + 2 r 0 r H } ee,cos (* — 2 ) 
[14] 
+ { r K r i + r 2 r 7 + r 5 r 3 } ee,cos ( 2 * — 2 ? + r) + {r 14 r, +r 2 r 6 + r 5 r 4 } e^cos (2t + x — z) 
[15] [16] 
+ {r<? + r 7 r 6 + e, 2 cos 2 z + {r 17 r, + r 5 r 6 } e, 2 cos {2t - 2 z) 
[17] [18] 
+ { r nr, + r 7 r 5 } e^cos (2 t + 2 2 ) + r JL. cos 4 t + ^ cos (4 * — 2x) 
[19] [131] " [132] 
From the preceding development that of r 4 may be easily inferred. 
r 4 = a 4 {1 + 5 e 2 — 4 e cos x -f e 2 cos 2 ;r} 
[ 0 ] [ 2 ] [ 8 ] 
Considering the terms only in R multiplied by ^ 
{1 + 3 cos (2 A — 2 A,) — 2s 2 } j" 
~~ m ‘ { 4 ( ! +V) r 7 ( 1 + 3 cos (2 X - 2 A,) — 2 s 2 } } 
neglecting s 4 
= { 4 ^ {1 {i- 5^3*'} 
37 = m /{;rs + ^1 [I +3cos(2x-2i,)j} s 
