184 OUTLINES OF NATURAL PHILOSOPHY. 



shewn by HALLEY to belong to all the satellites. 

 It lias also been found, that the eccentricity of Ju- 

 piter's orbit does affect the inequality in question. 

 MELANDERHJELM, Astron. vol. n. p. 584-. 



184. The same law connects together the pe- 

 riods of the satellites, and their mean distances 

 from Jupiter, which connects the periods of the 

 planets, and their mean distances from the 

 Sun ; that is, the squares of the former quanti- 

 ties are as the cubes of the latter. 



NEWTONI Princip. Math. lib. in. prop. 17. 



1 



185. The mean motion of the first satellite, 

 added to twice the mean motion of the third, 

 is equal to three times the mean motion of the 

 second. 



a. If m', m", m"' y are the mean motions of the first, 

 second, and third satellite of Jupiter, 



m' + 2 m'" = 3 m". 



b. Also if L', L", L'", are the longitudes of these sa- 

 tellites, I/ 3 L" + 2 L'" =180. Mechanique 

 Celeste, torn. I. p. 342. 



186. The orbits of the satellites are not in the 

 same plane with the orbit of Jupiter. 



This appears from the duration of the eclipses of the 

 same satellite, when compared with one another. 



The 



