34 ECLIPSES OF THE SATELLITES. [SECT. iv. 



inequalities afford the means, not only of ascertaining the 

 compression of Jupiter's spheroid, but they prove that his 

 mass is not homogeneous. Although the apparent diameters 

 of the satellites are too small to be measured, yet their per- 

 turbations give the values of their masses with considerable 

 accuracy a striking proof of the power of analysis. 



A singular law obtains among the mean motions and mean 

 longitudes of the first three satellites. It appears from obser- 

 vation that the mean motion of the first satellite, plus twice 

 that of the third, is equal to three times that of the second ; 

 and that the mean longitude of the first satellite, minus three 

 times that of the second, plus twice that of the third, is always 

 equal to two right angles. It is proved by theory, that if 

 these relations had only been approximate when the satellites 

 were first launched into space, their mutual attractions would 

 have established and maintained them, notwithstanding the 

 secular inequalities to which they are liable. They extend 

 to the synodic motions (N. 92) of the satellites ; consequently 

 they affect their eclipses, and have a very great influence on 

 their whole theory. The satellites move so nearly in the 

 plane of Jupiter's equator, which has a very small inclination 

 to his orbit, that the first three are eclipsed at each revolution 

 by the shadow of the planet, which is much larger than the 

 shadow of the moon : the fourth satellite is not eclipsed so 

 frequently as the others. The eclipses take place close to the 

 disc of Jupiter when he is near opposition (N. 93) ; but at 

 times his shadow is so projected with regard to the earth, 

 that the third and fourth satellites vanish and reappear on 

 the same side of the disc (N. 94). These eclipses are in all 

 respects similar to those of the moon : but, occasionally, the 

 satellites eclipse Jupiter, some times passing like obscure spots 

 across his surface, resembling annular eclipses of the sun, 

 and sometimes like a bright spot traversing one of his dark 

 belts. Before opposition, the shadow of the satellite, like a 

 round black spot, precedes its passage over the disc of the 

 planet ; and, after opposition, the shadow follows the satellite. 



