IN PHYSICAL ASTRONOMY. 
269 
— T,e ^r sin (2t + ^ — z — y) + + A r 6 1 ^ sin (2i + - 2 + y) 
[177] " [178] 
— T J1 e s sin (2 2 — y) + r -£- sin (2 2 + y) — ^ AZ sin; 2 * — 2 z — y) 
2 a°- 2 a? K y> 2 a* 
[179] 
[180] 
[181] 
+ ? f^ Sin ( 2t ~ 2z + y)~ 1 f e -^s\n(2t + 2z-y) + sin(2t + 2 z + y) 
[182] 
[183] 
[184] 
•li = (1 + | v . _ |) sin y + 3j^Z£ sin (x - y) + l^sin (x + ,) 
[146] [149] [150] 
3 m. aye, ■ , s , 3 m. aye. ■ , , s m. a y e 2 . , n > 
- , )g 3 — ' sin (2 -y) + — sin ( z + y) ^3— si n(2*-y) 
[155] ' [156] ' [161] 
,3 m.aye- ■ /rt , , , 9 in, ayee. ■ , . \ , 3 m.ayee.. , . , . 
+ — 5 — f- sin (2 x + y) + L — L — L sin (x + 2 — y) + — 4 — - sin (x + 2 + y) 
8 a, 3 4 a. 3 4 af 
[162] [167] [168] 
+ 9 -^Ap sin (, - 2 - y) + 3 y a y ee > Sin (. - 2 + y) - sin (2 2 - ,) 
[173] a> [174] ' [179] 
+ 9^p! sin(2z + y) 
[180] 
— = 1 + A e 2 -f- 3 e cos r + -c ! cos 2 x 
r 3 2 2 
r being the elliptic value of r. 
If 2 = a y 2 146 sin y + a y 2 147 sin (2 t — y) + ay 2 148 sin (2 t + y) & c. 
2 *_ //, , 3e‘ 2 \ ,3 
r 3 ~{( 1 + -2-) 2i46+ -2 
e -2 
3e 2 
150 —fT *149 
lXsi 
J a 2 
sm y 
[146] 
+ {( 1 + ~ 2 ~) z ^ + 2)51 2 ‘ 53 } sin (2 < — y) 
[147] 
+ {( l + T') Zl48+ IT 2152 + if 2 ' 54 } J sin(2< + 2/ ) 
[148] 
* This multiplication of 2 by r 3 may be effected at once by means of Table II. 
