18 CELESTIAL MECHANICS: LEVSCHNER 



with the results by Le Verrier; his value for the inequality is 906". 

 Cauchy's investigation is more fully elaborated by M. Puiseux in An- 

 nales de 1'Observatoire de Paris, Vol. VII. In Vol. VIII, ibid., Hoiiel 

 has recomputed the inequality. 



The development of the reciprocal of the distance was later extended 

 by Tisserand. 14 He shows that the development depending upon the 

 inclination and eccentricity is divergent in some parts of the orbit 

 of Pallas and proceeds to give the analytical development and to 

 apply it to the case of Pallas. 



In Bulletin Astronomique Vol. XII, 1895, M. P. Bruck has pub- 

 lished the results of his work on 'The secular variations of the ellip- 

 tic elements of Pallas due to the action of Jupiter." He used the 

 method developed by Gauss and extended by Hill and Callandreau. 

 He utilizes elements by Farley for the epoch 1878. 



In 1910 Georg^ Struve 15 published his results on "Die Darstellung 

 der Pallasbahn durch die Gauss'sche Theorie fur den Zeitraum 1803 

 bis 1910." The result of his work based on 63 normal places is a 

 more accurate value for the mean motion of Pallas (769".1385). 

 The new value for the annual motion of Pallas compared with Jupiter 

 becomes 18n' 7n = 123". The deviation between observation and 

 computation still amounts to 4' which is attributed to the second 

 order perturbations. These residuals are somewhat reduced by empiri- 

 cal terms. 



In A. N. No. 205, p. 225, M. Viljev has published his "Recherches 

 sur le mouvement de Pallas." He attempts to reduce the residuals 

 from Struve's work (4') by taking into account second order terms 

 in the general perturbations, employing the method by Hill. He 

 reports his results as negative. 



REFERENCES 



CODE'S A. J. 1805, p. 102. "British Nautical Almanac 1860 (not 



"BODE'S A. J. 1805, pp. 106, 111, 228. available here). 



"BoDE's A. J. 1805, pp. 181, 182. 13 Tisserand Merhaninup TpWp vol 



CODE'S A. J. 1806, pp. 179-180. ^c Mecnam <l u e Celeste, vol. 



'GAUSSWERKE. VOl. Vi, pp. 3-24. IV, P. ^/S. 



6 GAUSS WERKE. vol. vii, pp. 413-610. Annales de 1'Observatoire de Paris. 



'BoDE'sA. J. 1828, pp. 154, 157. vol. xv. 



"BoDE'sA. J. 1829, p. 158. "Dissertation Berlin. Ebernig, 1910 



B. J. 1837, pp. 24&-250. (not ava il a ble here) . 



* PP ' 



14329 



A B'. J. i851, pp. 547 and 549. A. N. A - J - B -> 1910 > P- 188 - 

 vol. 55, p. 194. B. A. 28, p. 184. 



