28 PERTURBATIONS OF THE SATELLITES. SECT. IV. 



traction, 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 perturbation 

 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 >' s . 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 satellites, 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 eccen- 

 tricity 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 displace- 

 ment of the orbit of Jupiter, and the variation in the 

 position of his equator, also aflfect 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 equa- 

 tor, 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 equa- 

 tor 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 inequalities afford the means, not 

 only of ascertaining the compression of Jupiter's sphe- 

 roid, but they prove that his mass is not homogeneous. 

 Although the apparent diameters of the satellites are 

 too small to be measured, yet their perturbations 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 observation that the mean motion of the first 

 satellite, plus twice that of the third, is equal to three 



