SECT, iv.] PERTURBATIONS OF THE SATELLITES. 83 



the influence of Jupiter's compression ; and they have a slow 

 motion corresponding 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 attraction the most remarkable take 

 place in the angular motions (N. 89) of the three nearest 

 to Jupiter, the second of which receives from the first a per- 

 turbation similar to that which it produces in the third ; and 

 it experiences from the third a perturbation similar to that 

 which it communicates to the first. In the eclipses these 

 two inequalities are combined into one, whose period is 

 437-659 da y g . The variations peculiar to the satellites arise 

 from the secular inequalities occasioned by the action of the 

 planets in the form and position of Jupiter's orbit, and from 

 the displacement of his equator. It is obvious that whatever 

 alters the relative positions of the sun, Jupiter, and his satel- 

 lites, must occasion a change in the directions and intensities 

 of the forces, which will affect the motions and orbits of the 

 satellites. For this reason the secular variations in the ex- 

 centricity of Jupiter's orbit occasion secular inequalities in 

 the mean motions of the satellites, and in the motions of the 

 nodes and apsides of their orbits. The displacement of the 

 orbit of Jupiter, and the variation in the position of his equa- 

 tor, also affect these small bodies (N. 90). The plane of 

 Jupiter's equator is inclined to the plane of his orbit at an 

 angle of 3 5' 30", so that the action of the sun and of the 

 satellites themselves produces a nutation and precession (N. 

 91) in his equator, precisely similar to that which takes place 

 in the rotation of the earth, from the action of the sun and 

 moon. Hence the protuberant matter at Jupiter's equator is 

 continually changing its position with regard to the satellites, 

 and produces corresponding mutations in their motions. 

 And, as the cause must be proportional to the effect, these 



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