CELESTIAL MECHANICS: LEUSCHNER 13 



widely from the mean mean motion. An arbitrary value was substi- 

 tuted. The Jupiter mass is taken to be 1/1047.355. The expressions 

 for the periodic terms of the perturbations are given. In order to 

 arrive at mean elements as well as to see how closely the perturba- 

 tions represent the observations, ten normal places 1802, 1807, 1830, 

 1857, 1863, 1866, 1873, 1883, 1885, 1890, were formed. Secular per- 

 turbations of Mars, Jupiter, and Saturn were computed by the method 

 of Gauss. The periodic perturbations by Mars and Saturn were taken 

 from the tables of Damoiseau. Preliminary elements and a least 

 squares solution led to mean Elements M. The residuals are 40" 

 to +40" in hel. longitude, 20" to +13" in geoc. latitude. Hill 

 originally intended to enlarge and complete his theory of Ceres; for 

 this purpose he collected the observations into 75 normals from 1801- 

 1897. 21 He published the positions because he did not expect to finish 

 the work. The collection is not complete. 



As an extension of Hill's work Merfield 22 has given a computation 

 of the secular perturbations of Ceres arising from the action of the 

 eight Major Planets. From Hill's theory and his mean elements 

 using the method of Gauss as set forth by Hill the numerical values 

 of the action of the planets were derived. 



M. Wolf 23 has developed the expression (p) according to the theory 

 of Gylden in the case of Ceres. Cf. Tisserand, Mecanique Celeste, 

 Vol. 4. 



M. Viljev 24 has published tables of absolute perturbations of Ceres 

 after the method of Hansen. 



REFERENCES 



'BODE'S B. J. 1804, p. 249. B. J. "B. J. 1831, p. 277. A. N. vol. 27, 



1805, p. 202. v. Zach, Monatliche p. 177. 



Correspondance. Not available here. 1<s Connaissance des Temps 1846. Ad- 



Lalande, Connaissance des Temps de ditions p. 32. Not available here. 



1'annee xiii. Witt, H.u. E. vol. 14. "A. J. vol. 3, p. 153; p. 162. 



BoDEsB. J. 1804, p. 255. "Nautical Almanac 1837. B. J. 1838, 



8 BODE s B. J. 1804, p. 256. D ose 



CODE'S B. J. 1804, p. 259. A ' T i , 



CODE'S B. J. 1805, p. 94. Gauss. M N vol 38 D 119 



Werke Bd. 6, p. 200. *> f ' T V o1 16 n ' 87 



GAUSS. Werke Bd. 6, p. 207. J J; * 3/51 



7 BODE'S B. J. 1805, p. 96. M fjf V l R7 P ' *ai 



8 A J vol 16 p 57 ' N< vo ' 67 ' p> 551< 



9 v.' Zach'. Monatliche Correspon- "WOLF. Bur les termes elemen- 



dance 1802, Dec. Not available here. taires dans I expression du rayon- 



10 GAUSS. Werke Bd. 7, p. 375. vecteur. Stockholm, 1890. 



11 GAUSS. Werke Bd. 7, p. 401. Publications de 1'Observatoire Cen- 

 13 A. N. vol. 7, p. 413. tral Nicolas, Poulkovo. Not available 

 18 B. J. 1830, p. 245. here. 



