FOURTH SECTION. 



ON THE DETERMINATION OF ORBITS, TAKING INTO ACCOUNT THE 



PERTURBATIONS. 



190. 



THE perturbations which the motions of planets suffer from the influence of 

 other planets, are so small and so slow that they only become sensible after a 

 long interval of time ; within a shorter time, or even within one or several entire 

 revolutions, according to circumstances, the motion would differ so little from the 

 motion exactly described, according to the laws of KEPLER, in a perfect ellipse, 

 that observations cannot show the difference. As long as this is true, it would 

 not be worth while to undertake prematurely the computation of the perturba 

 tions, but it will be sufficient to adapt to the observations what we may call an 

 osculating conic section: but, afterwards, when the planet has been accurately 

 observed for a longer time, the effect of the perturbations will show itself in such 

 a manner, that it will no longer be possible to satisfy exactly all the observations 

 by a purely elliptic motion ; then, accordingly, a complete and permanent agree 

 ment cannot be obtained, unless the perturbations are properly connected with 

 the elliptic motion. 



Since the determination of the elliptic elements with which, in order that the 

 observations may be exactly represented, the perturbations are to be combined, 

 supposes a knowledge of the latter; so, inversely, the theory of the perturbations 

 cannot be accurately settled unless the elements are already very nearly known : 

 the nature of the case does not admit of this difficult tusk being accomplished 

 with complete success at the first trial : but the perturbations and the elements 

 can be brought to the highest degree of perfection only by alternate corrections 

 (274) 



