CELESTIAL MECHANICS: LEUSCHNER 57 



(617) PATROCLUS, 1906 VY. 



Discovered by Kopff 1 at Heidelberg, October 17, 1906. 



Preliminary Elements A were computed by Heinrich 2 based on 

 four observations October 21 to December 7. 



From Elements A Charlier 3 has noted that the longitude of Pat- 

 roclus is approximately 60 behind Jupiter as compared with Achilles 

 and Hector which are approximately 60 ahead of Jupiter. From 

 the same elements, Stromgren 3 has made a similar comparison. 



A second set of preliminary Elements B were computed by Hein- 

 rich 4 by variation of the distances on the basis of five observa- 

 tions from 1906 October 21 to December 7. On page 339 of the 

 same reference the correction is made that Elements B refer to 

 equinox 1906. Elements B are used to compute the special per- 

 turbations, by the method of variation of the constants, and a third 

 set of Elements C with an ephemeris for 1907 is published. 5 A 

 continuation of the ephemeris is published on page 251 of the same 

 reference. Observations November 8 and 10, 1907, show the follow- 

 ing corrections to the ephemeris: Aa= 34 s A8= 0'.8. 



Ephemerides for the oppositions 1908, 1909, 1910, 1912, 1913, by 

 Heinrich 6 are based on Elements C. The correction to the ephemeris 

 in 1909 was A a 39 s and A8+3'.3. 



From 1914 to 1918 the ephemerides based on Elements C are 

 published in Kleine Planeten. 



An extensive application of Wilkens' method 7 for planets of 

 Jupiter's group, is made by Drucker. 8 He first takes Heinrich's Ele- 

 ments C as a basis for the computation of the perturbations due to 

 Jupiter and Saturn, by the method of variation of elements. Then 

 corrects Elements C on the basis of twelve normal places (1906 to 

 1918). See Elements D. The residuals for the twelve normal places, 

 from Elements D plus the special perturbations due to Jupiter and 

 Saturn, vary from 7".9 to +10".3 for Aa cos 8 and 4".8 to 

 +4".9 for AS. 



With Elements D the perturbations due to Jupiter and Saturn 

 are again computed and with the former twelve normal places and 

 a new thirteenth normal place, (1919), the Elements D were cor- 

 rected to a new set, E. With this new set of Elements E, and the 

 new perturbations, the residuals for the normal places vary from 

 3".4 to +3".5 for Aa cos 8 and from 2".8 to +2".9 for AS. He 

 states these Elements E may be considered as definite. In a foot- 

 note on page 27 of the same reference, the residuals for an observation 

 1920, December 16, are Aa cos 8 +4".4 and AS +1".4. The ephemeris 

 for 1920 was computed from Elements E, plus special perturbations 

 due to Jupiter and Saturn. 



