12 CELESTIAL MECHANICS: LEVSCHNER 



In B. J. for 1831 Encke 14 gives an ephemeris from new Elements 

 I of his own based on the oppositions 1820, 1821, 1822, 1825. 

 Jupiter mass 1/1053.924. Special perturbations by Jupiter only. 

 Representation: 



1820 1821 1822 1825 1827 1829 

 in a 6" +2" 4" 3" 2" 27" 

 in 8 0" 0" +6" +1" 0" 11" 



In B. J. 1832 to 1836 the ephemerides by Heiligenstein were published. 

 Later the computation by Encke and Wolfers was used to 1871. 



In the meantime Damoiseau 16 had given expressions for the per- 

 turbations containing a large number of terms but the individual 

 coefficients do not seem to be very exact, according to Hill. 



For the use of the American Ephemeris, E. Schubert 16 undertook 

 to correct the elements by 250 observations in 14 oppositions, 1832- 

 1854, using special perturbations of the elements by Jupiter as com- 

 puted by Encke and Wolfers but corrected for the secular variation 

 of the obliquity. 17 Elements J. Residuals in a 22" to +21", in 

 8 8" to +8" ; </> corrected according to A. J., Vol. 5, p. 73. A further 

 correction of the elements by Schubert 18 was based on only four 

 normal places in 1853, 1854, 1855, 1857; he applied the special per- 

 turbations of the elements by Jupiter and Saturn. Representation of 

 the normals 0", "by which the correctness of the whole is proved." 

 Elements K. 



Godward 19 repeats the process of Heiligenstein, Encke, Wolfers, 

 Schubert. The errors for fifteen oppositions 1857 to 1876 of the 

 ephemerides in Nautical Almanac which include the perturbations 

 of Venus, the Earth, Mars, Jupiter, Saturn gave by a least squares 

 solution the Elements L. Ephemerides by these elements were given 

 in the Nautical Almanac to 1913. 



The corrections to Encke's ephemerides increased after 28 years 

 to 3 8 in a 20" in 8. 



The corrections to Schubert's ephemerides increased after 23 years 

 to +6 8 in a 40" in 8. 



The corrections to Godward's ephemerides increased after 36 years 

 to +2 a in a 10" in 8. 



For the purpose of illustrating his modified form of computing 

 absolute perturbations Hill 20 computed the first order perturbations 

 of Ceres by Jupiter starting with the first elements by Schubert (un- 

 corrected). It was found that the osculating mean motion differed 



