288 OUTLINES OF NATURAL PHILOSOPHY. 



satellite is nearly equal to the Moon. Mecanique 

 Celeste, 2<k Partie, liv. 8. chap. 8. 



CONCLUSION. 



289. One general result of these investiga- 

 tions is, that both in the system of primary and 

 secondary planets, two elements of every orbit 

 remain secure against all disturbance ; the 

 mean distance, and the mean motion, or, which 

 is^the same, the transverse axis of the orbit, and 

 the time of the planet's revolution. Another 

 result is, that all the inequalities in the planet- 

 ary motions are periodical, and observe such 

 laws that each of them, after a certain time, 

 runs through the same series of changes. 



Every inequality is expressed by terms of the form 

 Asin?z or Acosnt; where A is a constant co- 

 efficient, and n a certain multiplier of t the time, 

 so that n t is an arch of a circle, which increases 

 proportionally to the time. Now, though n t is thus 

 capable of indefinite increase, yet since sin n t 

 never can exceed the radius or 1, the inequality 

 can never exceed A. Accordingly, the value of the 

 term A sin n t, first increases from to A, and their 

 decreases from A to ; after which it becomes ne- 

 gative, 



