28 CELESTIAL MECHANICS: LEUSCHNER 



(10) HYGIEA 



De Gasparis at Naples announced to the General-Secretary of Cor- 

 rispondenza Scientifica that he had discovered this planet April 12, 

 1849. The magnitude was 9-10. 1 



A large number of preliminary orbits were computed by Encke, 2 

 Luther, 3 Brorsen, 4 Quirling, 5 d'Arrest, 6 Hensel, 7 Santini, 8 from observa- 

 tions in the first opposition with mean motions ranging from 601" to 

 652". The first more certain, Elements A, were those by d'Arrest 9 

 from observations in 1849 and 1850. These elements were published 

 in B. J. 1853-55, brought forward with special perturbations by Jupiter. 



In B. J. for 1856 two sets of elements were published: one by Cheval- 

 lier at Durham, B, from observations in 1851 and 1852; and one, C, 

 by Zech at Tubingen. The latter (corrected for an error 10 which did 

 not affect the ephemeris) were based upon four oppositions and repre- 

 sented the opposition 1854 by +0 s -t> in a and 1" in 8. This was the 

 beginning of Zech's important work which made this planet suitable 

 for testing theories in the case of near commensurability. 



In B, J. 1858, new Elements D, by Zech, 11 are published, based upon 

 five oppositions taking the perturbations by Jupiter, Saturn, and Mars 

 into account. These elements are very closely the same as those v. 

 Zeipel selected from Zech's manuscript. In this the general perturba- 

 tions by Jupiter, Saturn, and Mars were computed and partly tabu- 

 lated. The basic elements for this computation were founded on 

 eight oppositions. After Zech's death in 1864 his computations of 

 the general perturbations of the planets (5) and (10) were discon- 

 tinued by the Recheninstitut, whereas his elements and special per- 

 turbations for (10) Hygiea were used in B. J. until 1875 by Powalky 

 and Becker. In 1873 the correction to the ephemeris had increased to 

 4 s in a and 20" in 8. 



In B. J. 1876 E. Becker published a preliminary set of elements which 

 finally was corrected to the Elements E, given by Bauschinger 12 based 

 upon the oppositions 1868, 1869, 1871, 1873 and 1874. Special per- 

 turbations by Jupiter and Saturn were included and brought forward 

 to the osculation 1898, December 20. 



The elements given in Kleine Planeten for 1920 are Becker's brought 

 forward by Strehlow with Jupiter's perturbations. The mean motion 

 is corrected empirically by +0"-07 (since 1898, August 22), represent- 

 ing the fourteen oppositions since 1900 within ztO^. Osculation 1920 

 January 0. Elements F. 



In the mean time v. Zeipel 13 had computed the tables for the general 

 perturbations by Jupiter according to the method by Bohlin in the case 



