SECT. IV. PERTURBATIONS OF THE SATELLITES. 29 



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. 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 excen- 

 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 displacement of the orbit of Jupiter, 

 and the variation in the position of his equator, 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 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 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 observa- 

 tion 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 



