669 



Öfversigt af Kongl. Vetenskaps-Akademiens Förhandlingar 1899. N:o 7. 



Stockholm. 



Meddelanden från Lunds Astronomiska Observatorium. N:o 8. 



Introduction of the argument Xm in the problem of 

 pertubations. 



By C. A. Schultz-Steinheil, 



(Communicated 1899 September 13 by C. V. L. Charher.) 



As far back as 1874 Gyldén devised a method of treating the 

 perturbative pi'oblem by means of which it is possible to develop 

 the perturbations after two arguments, one of which is constant 

 during half the tinie of the planet's revolution. Several astrono- 

 mers viz. Backlund, Bohlin, Callandreau and others have 

 afterwards successfully used this method in their calculations of 

 comets as well as planets, but oniy for evaluating relative 

 perturbations. Charlier, for the first time, has adopted the 

 method on absolute perturbations of a small planet, Thetis; he 

 made his calculations after formulas given by Hansen, and intro- 

 duced the argument after all integrations. There are, however, 

 several advantages one gains by introducing the argument be- 

 fore the integration. One of these is that on integrating we 

 then only have integers as divisors and consequently no small 

 divisors appear, and therefore this integration is easely per- 

 formed. Afterwards we have to determine the constants which 

 are functions of the introduced argument, and therefore con- 

 stant only during half a revolution. Here the small divisors 

 that did not occur during the integration appear on taking sums 

 of trigonometrical series. We may, however, arrange the formulas 

 so that no terms are enlarged by small divisors and then again 

 diminished by small factors, as is the case in Hansen's theory 

 of the small planets. 



