272 Prof. Encke on the Elements of the Planet Ceres. 



oppositions, seem to prove sufficiently that the equations for 

 the perturbations, if developed as is usual for the old planets, 

 would require to be extended considerably beyond the first 

 power of the eccentricity, if great accordance is intended. In 

 the same proportion, however, the calculation of a single place 

 would have become irksome, even taking into consideration 

 the facility afforded by the excellent construction of the tables 

 of perturbations (Zach'sCorresp. 1803, March); and therefore, 

 even if every part had already been perfectly developed, still 

 this method would hardly have deserved the preference on 

 the score of brevity of computation. 



As an interval of time, the number of one hundred days was 

 selected for this first approximation, and only the attraction of 

 Jupiter was taken into account. The mass of this planet was 



taken, according to Nicolai, at -rTTT-rr— . This value, which is 



-" o ' 1053"924 



one-eightieth part more than the old determination by Laplace, 

 appears in the cases of Pallas, Juno, and Vesta, to agree better 

 with the observations, and therefore seems likewise for Ceres 

 to deserve the preference. 



The four oppositions necessary for deducing the elements 

 were found to be, from the observations published, as follows : 



And proceeding from the elements at the moment of the first 

 opposition, the computations of the perturbations for the fol- 

 lowing ones gave the following corrections of the elements, in 

 which however the precession is still to be added to all the 

 longitudes. 



Correction. 



Mean Longitude ... = L = 

 Long, of Perihelion = w = 



Node =£3 = 



Inclination =: i ^ 



Angle of Eccentricity = <p = 

 Daily Sider. Motion = j£< = 



1822. 

 Aug. 22. 



+ 2 30-0 

 -32 47-9 

 — 41-9 

 + 8-3 

 + 1 12-9 

 + 0-70887 



1825. 

 March 14. 



+ 1 36-8 



— 107 55-7 



— 2 20-3 



— 19-1 



— 1 9-5 

 + 0-16263 



These 



