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revolution in 521 years, while those of Jupiter's orbit require no less than 36261 years,-a proof of the reciprocal attraction 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 disturbances they experience.
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 pertubation similar to that which it produces in the third; and it experiences from the third a pertubation 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 af
fect the motions and orbits of the satellites. For this reason the secular variation 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 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 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 pertubations 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 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, though not so immediately applicable to the wants of man, unfolds
one of the properties of light,-that medium without whose cheering influence all the beauties of the creation would have been to us a blank. It is observed, that those eclipses of the first satellite, which happen when Jupiter is near conjunction, are later by 16m 26s than those which take place when the planet is in opposition. But, as Jupiter is nearer to us when in opposition by the whole breadth of the earth's orbit than when in conjunction, this circumstance was attributed to the time employed by the rays of light in crossing the earth's orbit, a distance of about 190 millions of miles; whence it is estimated that light travels at the rate of 190000 miles in one second. Such is its velocity, that the earth, moving at the rate of 19 miles in a second, would take two months to pass through a distance which a ray of light would dart over in eight minutes. The subsequent discovery of the aberration of light confirmed this astonishing result.
Objects appear to be situate in the direction of the rays which proceed from them. Were light propagated instantaneously, every object, whether at rest or in motion, would appear in the direction of these rays; but as light takes some time to travel, we see Jupiter in conjunction, by means of rays that left him 16m 26s before; but, during that time, we have changed our position, in consequence of the motion of the earth in its orbit; consequently we refer Jupiter to a place in which he is not. His true position is in the diagonal of the parellelogram, whose sides are in the ratio of the velocity of light to the velocity of the earth in its orbit, which is as 190000 to 19. In consequence of the aberration of light, the heavenly bodies seem to be in places in which they are not. In fact, if the earth were at rest, rays from a star would pass along
the axis of a telescope directed to it: but if the earth were to begin to move in its orbit, with its usual velocity, these rays would strike against the side of the tube; it would therefore, be necessary to incline the telescope a little, in order to see the star. The angle contained between the axis of the telescope and a line drawn to the true place of the star, is its aberration, which varies in quantity and direction in different parts of the earth's orbit; but as it is only 20" 37, or 20"-5, it is insensible in ordinary cases.
The velocity of light deduced from the observed aberration of the fixed stars, perfectly corresponds with that given by the eclipses of the first satellite. The same result, obtained from sources so- different, leaves not a doubt of its truth. Many such beautiful coincidences, derived from circumstances apparently the most unpromising and dissimilar, occur in the rest of physical astronomy, and prove dependences which we might otherwise be unable to trace. The identity of the velocity of light, at the distance of Jupiter, and on the earth's surface, shows that its velocity is uniform; and if light consists in the vibrations of an elastic fluid or ether filling space, an hypothesis which accords best with observed phenomena, the uniformity of its velocity shows that the density of the fluid throughout the whole extent of the solar system must be proportional to its elasticity. Among the fortunate conjectures which have been confirmed by subsequent experience, that of Bacon is not the least remarkable. It produces in me,' says the restorer of true philosophy, 'a doubt whether the face of the serene and starry heavens be seen at the instant it really exists, or not till some time later; and whether there be not, with respect to the heavenly bodies, a true time and an apparent time, no less than