IN PHYSICAL ASTRONOMY. 
61 
+ “ ( 2 (r l3 + ^ (S£ b _^_ b #_ b \ 
' (3 re — 3re,) l V 2/ /*(2re-3n,) \4a, 2 3 ’ 2a/ 3 ’ 3 4fl ( 2 3 ' 4 / 
+ — ? . b, 3 "l e sin (2 re t — 3 re, t + 2 s — 3 s. + tu) 
p (re — re,) a, ’ 3 J 
i n / 0 | r 4 \ 4rez, re / 3 a- u a 3 L a- k \ 
+ (3 re - 4 re,) L V 14 + ~2 ) /x (3 re - 4 re,) \4V 3,3 2a/ ° 3 ’ 4 4a/ 2 ® 3 *y 
H m ,n a — 6, 4 1 e sin (3 re t — 4 re, £ + 3 e — 4 s + ot) 
j x (re — re,) a, ’ J 
2 re 
+ — r 15 e, sin (re, / + £, — tzr,) 
+ L / 2 r 17 - — 2m '” (^-b 3 l -^b 3 , 
(2 re — re,) l /x (2 re — re,) \4 a, 2 ’ 2 a, ’* 
— & 3)3 ^ | e, sin (2 re t — re, t + 2 s — £, — or,) 
[13] 
[14] 
[15] 
[ 17 ] 
Expression 
for the longi- 
tude when 
a < a,. 
re 1 
2r, 0 
3 m l re /3a 5 , 
- ^ i,. 
(3 re 
— 2 re ; ) 1 
^ ' 18 
jx (3 re — 2 re,) \4a, 5 3, “ 
2 a, 3,3 
a 2 
4 a, 
2 * 3 ’ 4 )} 
e, sin (3 re f — 2 re, / + 3 £ - 
- 2 £, - w,) 
[18] 
n J 
4 rei, re / 3 a 2 ^ 
_ a a 
(4 re 
-3re,)l 
| * 1 19 
/x (4 re — 3 re,) \4 a, 2 3,3 
2 a, 3,4 
a 2 
4 a, 
e, sin (4 re t — 3 re, f + 4 s ■ 
- 3 e, - w, 
[19] 
. M I 9, - 
t re, re /2 a 2 a 2 ^ 
^ A 
(re- 
2 «,) l ' 
w p, (re — 2 re,) \ a, 2 2 a, 2 
3,0 ^ 
+ T 
^ 4 “) 
j- e, sin (re f — 2 re, f + e — 
2 £, + «,) 
[20] 
re J 
2 r 
m, re ( — a ~ i 
° be , 
(2 re 
-3 re,) 1 
/x (2 re — 3 re,) \ 4 a, 2 
2 a, 3 ’ 2 
, 3 re 
4 a, 
!»»)} 
e, sin (2 re / — 3 re, Z + 2 £ - 
- 3 £, + ra-,) 
[21] 
n 
[ 2 r n: , 
m, re / a 2 ^ 
a . a a , 
(3 re 
-4 re,) 
/x (3 re — 4»,) \ 4 a, 2 
V. 2a< °3,3 
+ 15^)} 
e, sin (3 re t — 4 re, < + 3 £ - 
- 4e, + ®,) 
[22] 
The expression for the tangent of the latitude has already been given, p. 49. 
