38 



considered of the order ni®. Therefore in the above values of 2? 



and P quantities of the order m* are neglected. 



These values of /i and P are next to be sub-tituted in equation (c) 



1. Vt = — TT^-i sni (2 V - 20 = r, — sin (% -20 x 



(1 4 e cos (c— y)) by equat. (18) 



But sin (2v — 2 ^) = sin (2 ii~2mv + 4e??j. sin (f— ^r)) 



— sin (2 v— 2 mv) + Aem sin (►— t) cos (2 11—2 wt 



=r sin (21-— 2»ti') + 2 em sin (3 f -2 m v — •r) — 2em sin (v— 2wic +7r) 



sin (2 V — 2 wi ~) 



(2— 2m) e sin (3 r— 2 m i-— t) V 

 (2 + 2m) e sin (y —2 ?ft H- ^) j 



hence |^ = — ^^-"^ - (2-2m) e sin (3 y-2m .-t) 



consequently 



2— 2m 

 Pdi 3 m'' a 1 2—2 



^-^ cos (2v — 2 mi/) 



rrr T — r = — rr~ < — ,t — t e cos (.3 v — 2mi'— 5r) 



'III tf u^ ill \ 3 — 2m ^ ^ 



— r-^-TT- e cos ( K — 2m V + ■Z) 



1 — 2m ^ ■' 



Without considering the disturbing force of the Sun, we found 

 M being unity that h = -^ a (1 — e- ) = ^ a neglecting the se- 

 cond power of the excentricity. If therefore we make h = \a + h' 

 h' will be a quantity of the order of the disturbing force or of 

 m^ 



Also without the disturbing force of the sun, equation (c) 

 becomes 



d~- u , 1 



rfy* ih — 



