IN PHYSICAL ASTRONOMY. 
51 
^ = n (1 + 2r 0 ) i + £ + 2 (1 + r 0 ) ecos (1 + &) * + £ — nr,^ 
la R l6 e. cos (n t + £ — nr,) 
and neglecting the square of the disturbing force 
^ = n (l + 2 r 0 ) t + £ + 2 (1 + r 0 ) ecos (1 + fc) * + e — nr,^ 
— 7 Jli a R l6 e ( cos ( 1 + k) t + s — nr,^ 
If 
e ( ! + k) cos nr 2 = ( 1 + r 0 ) e cos nr, — — C aJ? , 6 e, cos nr, 
Z AO 
772 • 
e ( 1 + A) sin Wo = ( 1 + r 0 ) e sin nr, — a 7*16 e / sln 
A = w ( 1 + 2 r 0 ) t + £ 2 e sin ( 1 + k) t + £ — nr„^ 
772 
e ( 1 + r 0 ) cos nr, = e (1 + k) cos nr 2 + — ' a R, 6 e, cos nr, 
Z [A 
• 771 • 
e (1 + r 0 ) sin nr, = e (1 + k) sinnr 2 + —1 a ft, 6 e, sin si, 
Z AO 
i (1 + r 0 ) = e (1 + A) { 1 + ^a R I6 -^- cos (nr 2 - nr,) 
cos nr, = cosnr„ { 1 — ^La R, 6 cos (nr 0 — nr.) "I -f -^-a R, c -^- 
L2/x e J 2 m, e 
{ 1 ~^ aRl6 'l C ° S ( ' W ' 2 “ ^ 7*16 y sin w, 
cos nr, 
sin nr. = sin nr„ 
772 € 
sin (nr 2 — nr,) = R, 6 -± cos nr„ 
therefore neglecting the square of the disturbing force 
= — { 1 + — n> + a 7*16 — cos (nr — nr ) } 
a L 2 [a, e J 
= ± { i + Zh (2fCs J0 - A £! 4 , , _ * 6j0 + ^l 6s ,1 
a l ffc l a, 3 4 a/ 3,1 V 3,0 2 a/ 3,1 / 
. m, f a°- , .3 a 2 7 a , a 2 , 1 e. , . 1 
ft 1 4 a/ 3,2 4a/ 3,0 4 a, 3,1 8a/ 3,2 J e v " J 
e J , , wz. f a 3 7 3 a 2 , a 3 , e, , x 1 l 
a L ^ la, 3 3,0 4 a/ 3,1 4a/ 3,1 e v "j J 
H 2 
