CELESTIAL MECHANICS: LEUSCHNER 21 



Jupiter. Berliner Jahrbuch uses the elements by Nicolai until 1830. 

 Fifteen oppositions used: 1804-1823. Special perturbations by Jupiter, 

 (Saturn, Mars, negligible). Residuals in longitude 23" to +27", 

 still show a run with the period of Jupiter. (Elements G.) 



In 1832 new elements by Encke 8 were introduced, and are carried 

 forward with special perturbations to 1865 by Bremiker and Powalky, 

 for the ephemerides published 1832-1865. Perturbations by Jupiter 

 with mass, 1/1053.924. (Elements H.) 



Damoiseau 9 has published general perturbations in the Connais- 

 sance des Temps. 



Hind 10 took over the work started by Nicolai, Encke, and Bremiker, 

 to compute osculating elements for each opposition by special per- 

 turbations. The ephemerides are published in the Nautical Almanac, 

 and the Berliner Jahrbuch. As a basis for this work he derived new 

 elements. (Elements I.) 



An attempt to apply Hansen's method of determination of the 

 general perturbations was made by Berkiewicz, 11 starting with Hind's 

 elements. The perturbations of the first order with" regard to Jupiter, 

 Mars, and Saturn were determined, also the constants of integration 

 leading to a mean motion, 814".090. No comparison with the obser- 

 vations is attempted. 



Being aware that the corrections to the ephemerides computed 

 according to Hind had increased to 3' in 1887, Downing 12 undertook 

 to correct Hind's elements. The errors of the tabular heliocentric 

 places published in Greenwich Observations, 1864-1887, are discussed. 

 Equations for the longitude and latitude corrections were set up ex- 

 pressed in terms of corrections to the elements and combined to elimi- 

 nate the corrections to the radius vector. The mean motion is included 

 in the solution and receives by far the greatest weight. The represen- 

 tation of the oppositions show a pronounced run in Aa. These ele- 

 ments were used for the computation of the annual ephemerides to 

 1913 in the Nautical Almanac and to 1917 in the Berliner Jahrbuch. 

 (Elements J). Oppositions used: 1864-1887. Special perturbations 

 by Venus, the Earth, Mars, Jupiter, Saturn. Representation varies 

 from 3" to +4" in Aa cos 8, and 1" to +2" in AS. Large 

 residual (11") for 1874. Representation for 1890 is then in a+3", 

 in SihO" against 65" and 6", according to Hind's computations. 



Since 1917 Ephemeriden der Kleinen Planeten gives mean elements 

 by Boda 13 derived by the method of Brendel. (Elements K.) Mean 

 elements. Perturbations by Jupiter according to Brendel, A. N., Vol. 

 195, p. 417. Expected representation 0.5 to year 2000. Opposi- 

 tions not stated. 



