IN PHYSICAL ASTRONOMY. 
29 
s 147 [ee ; sin (4 t — x — 2 ) 
[138] 
+ { + {V- *,} + fA r '~ x -‘| (4 t + x+z) 
L *" [139] 
s 147 fee,sin (4 t —x — z) 
[140] 
+ {“P{ ri, “ Al ) + I^ r2Sl47 } ee/Sin ( 4t + x ~ 2 > 
L " [141] 
+ {— ^ { r i f — A i} + ^y 2 Si4 7 | e / 2sin ( 4f — 2z ) 
In order to verify the developments which have been given, suppose 
R = 38m L a l e cos (2 t-x) 
1 7 a? 
r5 — = e. rJ cos z 
r 1 
S\ = e^sinz 
neglecting c> s, 
Development 
° ,f Q- 
t being used in the sense nt — nj. 
$ R - _ g - 38 m,« _] e c CO s (2 t — x) r r J cos z + sin (2 t — x) X 3 sin z } 
17 a, 3 1 
-^ ee , J _ — r b ' cos (2t - x + z) - If r b ' cos (2 t-x- z) 
~ a* 1 l 17 17 
+ 12 x 5 cos (2 t - * + z) - X 5 cos (2 t - * - z) | 
_ a 2 |_38|r 5 '-A 5 |<?e / cos(2f-x + z) - || |r s ' + X 5 j ee, cos (2 t - x - z)| 
°’ L ^ [15] [12] 
which terms are in fact given in the development of h R, p. 11 and p. 10. 
