120 NEWTON S PKINCIPIA. 



minator 4 (n f n)* N 2 in which n and n are the mean 

 motions of the first and second satellite, and N a composite 

 quantity not materially differing from n , which differs 



hardly at all from -, inasmuch as n = 2 n , while n = 

 2t 



2 n&quot; (n&quot; being the mean motion of the third satellite) ; and 

 hence the above denominator becoming little or nothing, 

 the term is of large amount ; and so of 8 v, the variation of 

 the anomaly.* He accordingly undertook the laborious 

 task of examining this complicated subject by considering 

 all these quantities ; and he arrived at the discovery of, 

 among other inequalities, a retardation of Saturn s motion 

 of about 3&quot; 6&quot; yearly, and an acceleration in Jupiter s 

 motion of about V 18 &quot;. Another irregularity in Saturn s 

 motion with respect to the vernal and autumnal equinox 

 had been observed by astronomers in the last century, and 

 could not be explained. Laplace found this, like all the 

 rest, to follow from the Newtonian theory. In short, 

 when summing up the subject in one of his concluding 

 books, he naturally and justly exclaims, &quot; Tel a etc le 

 sort de cette brillante decouverte, que chaque difficulte 

 qui s est elevee, est devenue pour elle un nouveau sujet 

 de triomphe ; ce qui est le vrai caractere du vrai systeme 

 de la nature.&quot; f 



There is no sensible disturbance produced by any 

 of the satellites, except the moon, upon the motion of 

 their primaries, from the extreme smallness of their 

 masses compared with those of the sun and of their 

 primaries; for 8 r is equal to a series in which 



M M &quot;M&quot; C are actors ea term k m 



* Mec. Cel. liv. viii. ch. 1. 4. 



| Ibid. liv. xv. ch. 1 Syst. du Monde, liv. v. ch. 3. 



+ Ibid liv. vi. ch. 4. 



