CELESTIAL MECHANICS: LEUSCHNER 29 



of near commensurability, Hecuba group. As a test he applied his 

 tables to the orbit of (10) Hygiea and started with the Elements G (a) 

 from Zech's manuscript. These were first transformed to mean ele- 

 ments and then compared with nine oppositions from 18491884 

 with the aid of his tables. A least squares solution gave the corrected 

 Elements H. 



The work of computing tables after Bohlin's method for the Hecuba 

 group had also been undertaken by A. 0. Leuschner 14 and an appli- 

 cation to (10) Hygiea was made by Miss E. Glancy and Miss S. H. 

 Levy 14 . In order to compare the results with those of v. Zeipel, Miss 

 Glancy 15 used the Berkeley tables and after a comparison with nine 

 oppositions between 1849-1884 obtained the Elements I, starting with 

 the mean Elements G(b). Further comparisons were made by repre- 

 senting observations in 1910, 1914, 1917. The residuals before solution 

 from Zech's elements with the Berkeley tables were 11' to +10' in 

 the plane; from Zech's elements and v. ZeipePs tables 24' to +5'. 

 After Miss Glancy 's solution the residuals are 8' to +7', and after 

 v. Zeipel's solution 7' to +8'; but in 1917 they are +9' and +19' 

 respectively, apparently in favor of the Elements I and the Berkeley 

 tables. 



The residuals from Zech's elements and the Berkeley tables ( 11' 

 to +10') show a decided periodicity of 30 years, thus pointing to the 

 influence of Saturn. Later observations in 1917 and 1921 are repre- 

 sented much better (0' and +10') by the Berkeley tables and Zech's 

 elements than by any of the solutions. 16 The best future representa- 

 tion may be expected from Zech's elements G(b) and the Berkeley 

 tables. The residuals, probably chiefly due to Saturn, keep within 

 fixed limits 10'. The most obvious next step would be to correct 

 the residuals for some of the earlier oppositions by means of the per- 

 turbations of Saturn and Mars, available in manuscript in the Rechen- 

 institut. Until that shall have been done, no corrections should be 

 applied to Zech's elements, which appear to be the best available. 



REFERENCES 



*A. N. vol. 28, p. 391. "H. v. Zeipel, Angenaherte Jupiter- 



2 A. N. vol. 29, p. 15. storungen f iir die Hecuba-Gruppe. 



3 A. N. vol. 29, p. 49. Memoires de TAcademie des Sciences 

 *A. N. vol. 29, p. 81. de St. Petersburg, vol. 12, Nr. 11, 



6 A. N. vol. 29, p. 81. iqno 



6 A. N. vol. 29, p. 81, p. 126; vol. 30, ' .. . , a . 



p 320. "National Academy of Sciences. 



7 A. N. vol. 30, p. 81, p. 82. Memoirs, vol. 14, third memoir. 



8 A. N. vol. 30, p. 87. 15 A. J. vol. 32, p. 27. 



.f"2' V0 }' 81> P * 27 * " A> ' Leuschner Comparison of 



" A ' N 1 ^Q P ' -U7 theory with observation for the minor 



"VerSffentUchungen des astronomis- P lanets < 10 > H y iea and < 175 > Andr - 

 chen Recheninstituts zu Berlin. Nr. 16, mache. Proc. N. A. S., Washington, 

 p. 48. vol. 8, No. 7, p. 170. 



