1297 



R,= 



Si 

 ^i ]/ai 



where a^ is a constant, wliinli, in accordance with (B), is determined by 



Li' 



'aiV^ 



Further we put 



L/i 



Consequently r, is purely periodic, and we have 



a,"/^ = a,V. (1 -^ r,). 

 Therefore 



dvi 



da I 

 1(1+ Vi) — . 

 ai 



If then we introduce again 



where of course Tj requires the same correction 



ÖJTi'= O'i 



as Xi, and if we suppose the perturbative function Ri expressed in 



the variables Xi , jii, ai and ^ji, then the equations become 



(11) 



dXi 

 dx 



dli 



i di2, 



A di^^- 



=: (c.-x) (1 +vi) — 2{l+vifai ^ + è (1 ^nfvi 



Oai 



A dRi 



cos 



djii ' 

 (fii dRi 



=3(cv-x)(l f.v)-2(l+rO'ai^-(H r,y . 



«T Oai iii On^ 



djti 

 dx 



d 



(12) 



I 1 dRi 

 ^dRi 



dx 11 i O.T,- 0^,- 



Of the first three equations we can arbitrarily choose two for use 

 in the computations. The simplest formulas are found if we use 

 A, and :nri. 



Instead of /?, (a;) I now introduce the constant fi,, which is 

 determined by 



— 1 A^(l+ ^^i.) 

 ' ' ~ a.' {ci—xy ' ,' * ' 



Further we put 



(13) 



