28? 



r 



(20) 



I. dl_i3,'m dS' dL _dS' 

 dt ~~ ~iy ~ dL 'dt~'W 



dg _ dS' dG _ dS' 



dt ~ dG dt ~ d;f 



dd^_ dS' d0_dS' 



dt ~~~J& ~dt~dd^ 



II. Pul U =z~^ + AU 



«o 



U ,/ ^ G 



r = (1 — e cos n) VI — e" = — 



ayw ^ ' u 



da k AU{l-e') dS dU AU dS \ 



-— = -— H cos n — ^—r — = e U sin u + -^-- \ 



dt Ur mr^ e dU dt mr' ' du j 



(27) 



dg LU\/{—e^ ds dG dS 



cos n — 



dt mr' e dG dt dg 



d{h_ dS dO _dS 



dt ~ öö . dt ~~ dlh 



If at t — O we start with A ^ = O, and if S = 0, then the 

 motion is Kepleiian : U, G, 0,<j, ^ are constants. In the general case, 

 when S differs from zero, AU is of the order of S, i. e. of the 

 order of the perturbing masses. 



III. Put F= V.-i-AV 



a{l-e') ,. G-AV 



(28) 



. A V again is of (he order of the perturbing masses. For S' =r 

 the motion is Keplerian and V, G, 0, g, \h are constants. 



In all cases the ciioice of the original variables .Ti,yi, is of course 



