1295 



It is usual to take j?/" := /mj (1 -f- ??i/). By keeping ^?, indeterminate 

 we have a parameter at our disposal, which can afterwards be so 

 chosen that the intermediary orbit assumes the desired form. 



I now introduce instead of //, gi, ihi, Li, Gi, Oi the canonical set 

 /,• z= li -f gi 4- &i , /,- , ifjj = — a^i , 

 'Gi , Hi = Li-Gi , Ti=zGi—0i 



Then we have 



where 



dGi~[dGiJ~^ Gid^i' 



(9) 



. . . / 2¥7 



Yi = 2 sm ^1,= ^ — -- . 



The second term is of the second degree in ;',, and conseqiientlj 

 very small. If now we put 



;,• = ;,•' + Ö/, 

 and if we determine Oi by 



dOi _ ^ Yi dSi' 

 It ~ ^ Wi öy7' 

 then we have 



dii'_^i* rbsr 



'df~Li'~\dGi^ 



where the parentheses denote that S'i must not be differentiated 

 with respect to G, so far as it depends on Gi through the incli- 

 nations Yi- This being agreed upon, we can omit the accent of 



k'i and the parentheses of j — ^ j, if we apply to the value of Aj so 



\(fGiJ 



determined the coiTection 



(fXi = ai (10) 



where (>i is determined from (9). 



In the theory of the inclinations the approximate commensura- 



bility does not give rise to particular difficulties. For this theory 



the most important point is to choose the plane of (x y) so that 



the inclinations of the satellites and of the equator always remain 



small. I will not enter upon this problem here, and I will further 



exclusively consider the four elements 



89* 



