IN PHYSICAL ASTRONOMY, 
31 
which terms are found in the development of & d R. These terms are in fact 
multiplied by n which is equal to m if n be taken equal to unity. 
d . (**) 
- — s s = " • ^ m ‘ a - y 2 s 147 cos (2 t + y) sin (2 t — y) 
11 af 
d s 
= ^fr i -{ + ^ s i47y 2sin4i -^«i47y 0 -s'n2y| 
[131] [62] 
which terms are found in the development of h 
T{/( d d?) d, r=^ 
81 e 2 
9 e 2 
128(1 -to) 2 32(2-2 m - c)- 32(2-2to + c ) 2 
9 e 2 . 9 a 2 , 9 
+ 
+ 
128(2- 3 w) 2 128(2 — to) 2 16(1 -to) 2 a/ 2 16(1 -to) 2 a/ 2 
— cos 2 t 
-{ 
4(2 — 2 m — c) 4 (2 — 2 m + c) J 8 ( 1 — to) 
J 8(1 - 
[1] 
ecos;r 
_ / 3 _ 21 | 3_ 
18(2 — m) 8 (2 — 3 m) / 8 (1 — to) 
e t cos z 
[5] 
+ 
I- 
27 
+ 
[ 2 ] 
45 
1 6 (2 — 2 m — c) (2 — 2 to + c) 64(1 — m) (2 — 2 to — 2 c) 
9 
32 (1 — to) (2 — 2 to + 2 c) 
e- cos 2 x 
[ 8 ] 
+ 
{"W 
+ 
TO + c) 8 ( 
63 \ 3 
(2 - 3 to - c) J 8(1- 
+ 
63 
c) J 8 ( 1 — to) 32 (2 — 2 to + c) (2 — 3 to) 
+ 
+ 32 (2 — 2 to - c) (2 - to) } e e ‘ C0S + 2 ) 
[11] 
h. + £ j 3 
[ L 8 (2 - 3 m + c) 8 (2 — to - c) J 
+ 
{- 
21 
3 m + c) ’ 8 (2 
9 
32 (2 — to) (2 — 2 to + c) 
63 
189 
+ 
64 (2 — to) (2 — 3 to) 64 ( 1 — to) (2 — 4 to) 
c)J 8(1— to) 32 (2 -3 to) (2 — 2 to - c) 
fee, cos (x — z) 
[14] 
} e, 2 cos 2 z 
[17] 
153 
