1158 



The third line contains the complementary part of the perturbative 

 function. The coefficients (2"'", differ from those of the usual develop- 

 ment by the introduction of the terms with Jj and Kj. The values 

 of (6',f and O"'" have been eiven in Leiden Annals XTI, J, pages 22 



^ '<i 9,9 



and 23. 



For the determination of the intermediary orbit we only use the 

 non-peiiodic part [Ri] of the perturbative function. We add to this 

 those terms of the secular part of the perturbative function corre- 

 sponding to the action of the sun, which do not contain angular 

 elements of the sun. These are with sufficient approximation 



where e, is the excentricity and i„ the inclination of the sun's orbit. 

 The perturbative function is developed in powers of t?, . For this 

 reason I have also, instead of ?j, , taken as unknown /?, = ï^, ^^l—^>i,^ 

 The equations determining m and e^ then become, instead of (18) 

 and (19): 



Ö [Ki] 



da 



|xe,* = 



, d\Ri] 



«,• 



If we denote by \R!i\ the non-periodic terms of the principal and 

 complementary parts of the pei'turbative function, these equations 

 become 



-^ - [/. + è ^.] - (1^. + |^.)e,' - ^ r^ Tï + 

 1 — (Lt, l-^nxi A 



_j 1 a, ^ = U . . (I) 



4 (a—x ) ( 1 —m) {ci—y. ) (1 — fi.) oai 



Aiei + 2{ci—yc)(\-iii)Jiei'^il-he.')-\^-0. . (2) 



(c, — x) (1 — ui) ,, a,* 



The tirst equation gives fi'i= — *- — • Then we ünd a, from 



1— fi, 



a.«(c,_xr =.(1 +m,)(l +M.')- 



