58 



CELESTIAL MECHANICS: LEUSCHNER 



Then he derives corresponding elements in Wilkens' system, Ele- 

 ments F and G. Elements F correspond to Elements D, and Elements 

 G correspond to Elements E. He states that it was only necessary 

 according to Wilkens' method to compute Elements F. 



He now computes positions (a and 8), for the thirteen normal 

 places, (1) from Elements E, with special perturbations due to 

 Jupiter; (2), the same places from Elements E without perturba- 

 tions; (3), the same places from Elements G without perturbations; 

 (4), the same places from Elements E with special perturbations due 

 to Jupiter and Saturn. A comparison is then made between the posi- 

 tions computed by the various systems, (1), (2), (3), (4). The table 

 of differences shows that Saturn's perturbations do not become ef- 

 fective until 1918. It shows, as we should expect, that for the period 

 of osculation, the various systems give the same results. It finally 

 shows that positions computed from (3) come closer to those com- 

 puted by (1), than the places computed by (2). 



Finally he computes the special perturbations due to Jupiter, by 

 the variation of elements, with the aid of Elements G and shows 

 that they are of the same order as those computed with Elements E. 



The ephemerides published in Kleine Planeten for 1920 and 1921 

 are based on Elements E, plus special perturbations due to Saturn 

 and Jupiter. J^^ ^ ^ f( 



An ephemeris for the opposition using Elements Ts^ 19l8-1919, 

 was computed by Paul Maitre. 9 Ephemerides for oppositions 1919- 

 1920, 1920-1921, and 1922, are also published by Drucker. 10 



REFERENCES 



A. N. vol. 172, p. 387. 



A. N. vol. 175, p. 87. 



A. N. vol. 175, p. 89. 



A. N. vol. 175, p. 291. 



A. N. vol. 176, p. 193. 



A. N. vol. 179, p. 223 vol. 180, p. 



45 vol. 183, p. 207 vol. 190, p. 395 

 vol. 194, p. 208. 



7 A. N. vol. 205, No. 4906. 



8 A. N. vol. 214, No. 5114. 

 9 Cir. O. M. No. 85, 1918. 



10 B.-Z. der A. N. No. 14, 1919-No. 

 48, 1920 No. 1, 1922. 



TABLE 15. Elements (617) Patroclus (1906 VY) 



