685 



Öfversigt af Kongl. Vetenskaps-Akademiens Förhandlingar 1901. N:o 9. 

 Stockholm. 



Meddelanden från Lunds Astronomiska Observatorium. N:o 19. 



Contributions to the theory of the secular pertur- 

 bations of the planets. 



By C. B. S. Ca VALLIN. 



(Communicated 13 November 1901 by C. V. L. Charlier.) 



The fundamental forraulas, from which this researcli issues, 

 are the follovving: 



1 



e cos 7t = ^ Ai cos (gjf + ßj) 



and , (I) 



e sin 7r = ^ Ai sin (git + ßi) 

 1=1 } 



where e denotes the excentricity and tv the longitude of the per- 

 helion of the planet in question, t the time and the A, g and ß 

 are certain real constants, the former being positive. 



The question is to determine e and tt as functions of t. 



When one of the constants A, say Ar, satisfies the con- 

 dition 



Ar> A^ + A2+ .. . + Ar -I + Ar + l + . . . + A„ {T) 



it is easy to show that, for all <, 



yr = g^,t + a finite function. (I") 



In this case (7,. is the niean velocity with which tt increases 

 with t. 



