IN PHYSICAL ASTRONOMY. 
5 
+ {r 5 r, + 2 r 0 r 7 } e, cos (2 t + z) + {t\ 2 2 + r 4 r 3 + r, r 9 + r,r 10 }e 2 cos2x 
[7] [8] 
+ { ?, 2 r s + 2 r 0 r 9 } e 2 cos (2t — 2x) + {r 4 r 2 + 2 r 0 r 10 }e 2 cos (2 i + 2 x) 
[9] [10] 
+ + r i r ii + r i T b + r eU + r 3 r-j + 2 r 0 r n ] <?e,cos (x + z) 
[11] 
+ { r u7 , i + r 2 r 6 + r b r 3 + 2r 0 r ls } ee i cos (2 t — x — z) 
[12] 
+ {r u r, + r 2 r 7 + r 5 r 4 + 2r 0 r 13 } ee, cos (2 t + x + z) 
[13] 
+ { r ie r i + r i 5 r i + r z r i + r 6 r 3 + »' 7 r 4 + 2 r 0 r 14 } e e i cos (x — z) 
[14] 
+ + r 2 r 7 + r 3 r 3 } ee,cos (2 t — x + 2 ) + {r^r, + r 2 r 6 + r 5 r 4 } ee,cos (2 < + x — 2 ) 
[15] [16] 
+ {** + r 7 r 6 + r,r w + r,r 19 } e* cos 2 z + {r I7 r, + r 5 r 6 } e, 2 cos (2* - 2 z) 
[17] [18] 
+ { r n r i + r 7 r s} e / 2cos (2< + 2 2 ) + r -l- cos 4t + ^cos (4* — 2x) 
[19] [131] [132] 
From the preceding development that of i 4 (% may be easily inferred. 
r 4 = a 4 { 1 + 5 e 2 — 4 e cos x + e 2 cos 2 x} 
[0] [2] [8] 
Considering the terms only in R multiplied by — s 
R=z ~ m ‘{i^ (1 + 3cos (2A-2A,) -2s 2 }} 
~ ~ m ‘ { 4 (T + s 2 ) r} (1 +3 cos (2 A - 2 A,) -2s 2 }} 
neglecting .s 4 
= {—{l +3cos(2X-2A ; )} {1-5 2 }-^s 2 } 
d R f r 2 , r- r , ] 
dT 2 ~rj 1 1 F 3 cos (2 A — 2 A,)} j s 
