SECT. IV. EFFECTS OF JUPITER'S COMPRESSION. 27 



effect of this disturbing force in the spheroid of Jupiter 

 is, to occasion a direct "motion in the greater axes of the 

 orbits of all his satellites, which is more rapid the 

 nearer the satellite is to the planet, and very much 

 greater than that part of their motion which arises from 

 the disturbing action of the sun. The same cause 

 occasions the orbits of the satellites to remain nearly in 

 tho plane of Jupiter's equator (N. 87), on account of 

 which the satellites are always seen nearly in the same 

 line (N. 88) ; and the powerful action of that quantity 

 of prominent matter is the reason why the motions of 

 the nodes of these small bodies are so much more rapid 

 than those of the planet. The nodes of the fourth 

 satellite accomplish a tropical revolution in 531 years ; 

 while those of Jupiter's orbit require no less than 

 36,261 years ; a proof of the reciprocal attraction be- 

 tween each particle of Jupiter's equator and of the 

 satellites. In fact, if the satellites moved exactly in the 

 plane of Jupiter's equator, they would not be pulled 

 out of that plane, because his attraction would be equal 

 on both sides of it. But, as their orbits have a small 

 inclination to the plane of the planet's equator, there 

 is a want of symmetry, and the action of the protuberant 

 matter tends to make the nodes regress by pulling the 

 satellites above or below the planes of their orbits ; an 

 action which is so great on the interior satellites, that 

 the motions of their nodes are nearly the same as if no 

 other disturbing force existed. 



The orbits of the satellites do not retain a permanent 

 inclination, either to the plane of Jupiter's equator, or 

 to that of his orbit, but to certain planes passing between 

 the two, and through their intersection. These have a 

 greater inclination to his equator the farther the satel- 

 lite is removed, owing to the influence of Jupiter's 

 compression ; and they have a slow motion correspond- 

 ing to secular variations in the planes of Jupiter's orbit 

 and equator. 



The satellites are not only subject to periodic and 

 secular inequalities from their mutual attraction, similar 

 to those which affect the motions and orbits of the 

 planets, but also to others peculiar to themselves. Of 

 the periodic inequalities arising from their mutual at- 



