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moons only extends to a few centuries, it may be regarded as an epitome of that grand cycle which will not be accomplished by the planets in myriads of ages. The revolutions of the satellites about Jupiter are precisely similar to those of the planets about the sun it is true they are disturbed by the sun, but his distance is so great, that their motions are nearly the same as if they were not under his influence. The satellites, like the planets, were probably projected in elliptical orbits, but the compression of Jupiter's spheroid is very great in consequence of his rapid rotation; and as the masses of the satellites are nearly 100000 times less than that of Jupiter, the immense quantity of prominent. matter at his equator must soon have given the circular form observed in the orbits of the first and second satellites, which its superior attraction will always maintain. being farther removed from its influence, move in orbits with a very small eccentricity. The same cause occasions the orbits of the satellites to remain nearly in the plane of Jupiter's equator, on account of which they are always seen nearly in the same line; and the powerful action of that quantity of prominent matter is the reason why the motions of the nodes of these small bodies is so much more rapid than those of the planet. The nodes of the
The third and fourth satellites
fourth satellite accomplish a tropical revolution in 531 years, while those of Jupiter's orbit require no less than 36261 years,-a proof of the reciprocalattraction between each particle of Jupiter's equator and of the satellites. Although the two first satellites sensibly move in circles, they acquire a small ellipticity from the perience.
disturbances they ex
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 satellite is removed, owing to 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 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 437.659days. 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. this reason the secular variations in the eccentricity 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. The plane of Jupiter's equator is inclined to the plane of his orbit, so that the action of the sun and of the satellites themselves produces a nutation and precession in his equator, precisely similar to that which takes place in the rotation of the earth, from the action of the sun and moon, whence the protuberant matter at Jupiter's equator is continually changing its position with regard to the satellites, and produces corresponding muta
tions 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 three first satellites. It appears from observation 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 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 they are frequently eclipsed
by the shadow of the planet. The eclipses take place close to the disc of Jupiter when he is near opposition; but at times the 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. These eclipses are in all respects similar to those of the moon; but, occasionally, the satellites eclipse Jupiter, passing like black spots across his surface, and resemble annular eclipses of the sun. The instant of the beginning or end of an eclipse of a satellite marks the same instant of absolute time to all the inhabitants of the earth; therefore, the time of these eclipses observed by a traveller, when compared with the time of the eclipse computed for Greenwich, or any other fixed meridian, gives the difference of the meridians in time, and consequently the longitude of the place of observation. It has required all the refinements of modern instruments to render the eclipses of these remote moons available to the mariner; now, however, that system of bodies invisible to the naked eye, known to man by the aid of science alone, enables him to traverse the ocean, spreading the light of knowledge and the blessings of civilization over the most remote regions, and to return loaded with the productions of another hemisphere. Nor is this all: the eclipses of Jupiter's satellites have been the means of a discovery which,