CELESTIAL MECHANICS: LEUSCHNER 



55 



eleven normal places were formed, weighted according to number of 

 observations in each. 



The residuals, (freed from perturbations), for the 1906 and 1907 

 normal places are small. For normal place X, (1913), AacosS 

 +2781".2, AS + 1685".0; for normal place XI, (1914), Aa cos 8 

 +1664".!, A8+852".7. The resulting orbit improvement gave Ele- 

 ments F. The residuals for the normal places from Elements F vary 

 from + 19".8 to 40".9 in Aa cos 8, and 9".2 to +23"8 in A8. 

 With Elements F the special perturbations were recomputed by J. 

 Braae. With Elements F and the new perturbations, new residuals 

 for the normal places were determined and the orbit improved on this 

 basis. When the corrections to the elements were put back into the 

 equations of condition, the residuals were of the same order as prior to 

 the solution. Miss Hansen concludes a normal place must be incor- 

 rect. The equations of condition were again solved, with the last 

 normal place omitted. The resulting Elements G represent the ten 

 normal places in Aa cos 8 1".5 to +5".8 and A8 1".3 to +2".3. 



The normal place XI gives residuals Aa cos 8 1817".2, A8 

 1172".0, which indicates that it does not belong to Achilles. 



The special perturbations due to Jupiter for 1915 to 1920 are pub- 

 lished by Miss Hansen. 17 They were computed from Elements G. 

 These elements are published and utilized in Kleine Planeten since 

 1920. In Ark. for Math. Bd. 4 Nr. 20 Linders developed the approxi- 

 mate theory for planets near the libration points and gives the prin- 

 cipal perturbations of the elements of 588. Cf. Heinrich V. J. S. 1913. 



REFERENCES 



1 A. N. vol. 170, p. 353. 



2 A. N. vol. 171, p. 11. 



8 A. N. vol. 171, p. 127. 



4 A. N. vol. 171, p. 213. 



5 Meddelanden fran Lunds Observa- 

 torium, No. 18. 



Nat. Rund. vol. 21, p. 485^86. 

 7 Observatory, vol. 29, p. 352-355. 

 Pop. Ast. vol. 14, p. 472-475. 

 8 H. u. E. vol. 18, p. 517-521. 



Ciel et Terre. vol. 27, p. 161-164. 



10 A. N. vol. 174, p. 45-48. 



11 A. N. vol. 174, p. 175. 

 "A. N. vol. 180, p. 295. 



13 B. J. 1914, p. 30. 



14 L. O. Pub. vol. vii, p. 455. 

 15 In Manuscript (Berkeley). 



18 Pub. og mindre Meddelelser fra 

 Kobenhavns Obs. No. 37. 

 17 A. N. vol. 208, p. 345. 



TABLE U. Elements (688) Achilles (1906 TG.) 



