THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



JULY 1847. 



I. On the Perturbations of Planets moving in Eccentric and 

 Inclined Orbits. By Sir J. Lubbock, Bart.i F.R.S.* 



nPHE accuracy of the tables which give for an indefinite 

 -*■ time the places of the older planets, is at present sufficient 

 for the purposes of astronomy, and is commensurate with the 

 accuracy of observation ; or if this statement appears to be 

 exaggerated, it will at least be admitted that the sensible 

 errors which remain are owing rather to inadvertence in the 

 numerical computation than to the imperfection of the method 

 itself. Such a result is owing to the uninterrupted labours of 

 the greatest mathematicians from the time of Newton, and is 

 justly regarded as one of the greatest triumphs of human in- 

 telligence. But it must be recollected that these methods, 

 by which the perturbations of the older planets have been 

 obtained, are applicable only to the case of orbits nearly cir- 

 cular, and little inclined to each other; so that the general 

 solution of the problem of the three bodies, as it is called, 

 remains to the present day imperfect. The methods in use 

 for the older planets are founded, as is well known, upon the 

 development of the disturbing function in terms of the mean 

 anomalies. M. Binet has indeed carried this development to 

 quantities of the seventh order inclusive ; but such a de,velop- 

 ment is quite insufficient in the case of comets or planets 

 moving in highly eccentric and inclined orbits, which problem 

 presents far greater difficulty ; while the nature of the expres- 

 sion is such, that it is evidently impracticable to carry further 

 such a mode of development, even if the expressions were suf- 

 ficiently convergent when the eccentricity passes a certain 

 limit. 



The only memoir with which I am acquainted which pro- 



* Communicated by the Author. 

 Phil. Mag. S. S. Vol. 31. No. 205. Juli/ 1847. B 



