general laws by which their motions are governed, to the great system in which the sun acts the part of the primary, and the planets of its satellites. In each of these systems the laws of Kepler are obeyed, in the sense, that is to say, in which they are obeyed in the planetary system— approximately, and without prejudice to the effects of mutual perturbation, of extraneous interference, if any, and of that small but not imperceptible correction which arises from the elliptic form of the central body. Their orbits are circles or ellipses of very moderate excentricity, the primary occupying one focus. About this they describe areas very nearly proportional to the times; and the squares of the periodical times of all the satellites belonging to each planet are in proportion to each other as the cubes of their distances. The tables at the end of the volume exhibit a synoptic view of the distances and periods in these several systems, so far as they are at present known; and to all of them it will be observed that the same remark respecting their proximity to their primaries holds good, as in the case of the moon, with a similar reason for such close connection.

(534.) Of these systems, however, the only one which has been studied with attention to all its details, is that of Jupiter; partly on account of the conspicuous brilliancy of its four attendants, which are large enough to offer visible and measurable discs in telescopes of great power; but more for the sake of their eclipses, which, as they happen very frequently, and are easily observed, afford signals of considerable use for the determination of terrestrial longitudes (art. 266.). This method, indeed, until thrown into the back ground by the greater facility and exactness now attainable by lunar observations (art. 267.), was the best, or rather the only one, which could be relied on for great distances and long intervals.

(535.) The satellites of Jupiter revolve from west to east (following the analogy of the planets and moon,) in planes very nearly, although not exactly, coincident with that of the equator of the planet, or parallel to its belts. This latter plane is inclined 3° 5' 30" to the orbit of the planet, and is

therefore but little different from the plane of the ecliptic. Accordingly, we see their orbits projected very nearly into straight lines, in which they appear to oscillate to and fro, sometimes passing before Jupiter, and casting shadows on his disc, (which are very visible in good telescopes, like small round ink spots, the circular form of which is very evident,) and sometimes disappearing behind the body, or being eclipsed in its shadow at a distance from it. It is by these eclipses that we are furnished with accurate data for the construction of tables of the satellites' motions, as well as with signals for determining differences of longitude.

(536.) The eclipses of the satellites, in their general conception, are perfectly analogous to those of the moon, but in their detail they differ in several particulars. Owing to the much greater distance of Jupiter from the sun, and its greater magnitude, the cone of its shadow or umbra (art. 420.) is greatly more elongated, and of far greater dimension, than that of the earth. The satellites are, moreover, much less in proportion to their primary, their orbits less inclined to its ecliptic, and (comparatively to the diameter of the planet) of smaller dimensions, than is the case with the moon. Owing to these causes, the three interior satellites of Jupiter pass through the shadow, and are totally eclipsed, every revolution; and the fourth, though, from the greater inclination of its orbit, it sometimes escapes eclipse, and may occasionally graze as it were the border of the shadow, and suffer partial eclipse, yet does so comparatively seldom, and, ordinarily speaking, its eclipses happen, like those of the rest, each revolution.

(537.) These eclipses, moreover, are not seen, as is the case with those of the moon, from the center of their motion, but from a remote station, and one whose situation with respect to the line of shadow is variable. This, of course, makes no difference in the times of the eclipses, but a very great one in their visibility, and in their apparent situations with respect to the planet at the moments of their entering and quitting the shadow.

(538.) Suppose S to be the sun, E the earth in its orbit. EFGK, J Jupiter, and a b the orbit of one of its satellites

The cone of the shadow, then, will have its vertex at X, a point far beyond the orbits of all the satellites; and the

penumbra, owing to the great distance of the sun, and the consequent smallness of the angle (about 6' only) its disc subtends at Jupiter, will hardly extend, within the limits of the satellites' orbits, to any perceptible distance beyond the shadow, for which reason it is not represented in the figure. A satellite revolving ftom west to east (in the direction of the arrows) will be eclipsed when it enters the shadow at a, but not suddenly, because, like the moon, it has a considerable diameter seen from the planet; so that the time elapsing from the first perceptible loss of light to its total extinction will be that which it occupies in describing about Jupiter an angle equal to its apparent diameter as seen from the center of the planet, or rather somewhat more, by reason of the penumbra; and the same remark applies to its emergence at b. Now, owing to the difference of telescopes and of eyes, it is not possible to assign the precise moment of incipient obscuration, or of total extinction at a, nor that of the first glimpse of light falling on the satellite at b, or the complete recovery of its light. The observation of an eclipse, then, in which only the immersion, or only the emersion, is seen, is incomplete, and inadequate to afford any precise information, theoretical or practical. But, if both the immersion and emersion can be observed with the same telescope, and by the same person, the interval of the times will give the duration, and their mean the exact middle of the eclipse, when the satellite is in the line S J X, i.e. the true moment of its opposition to the sun. Such observations, and such only, are of use for determining the periods and other particulars of

the motions of the satellites, and for affording data of any material use for the calculation of terrestrial longitudes. The intervals of the eclipses, it will be observed, give the synodic periods of the satellites' revolutions; from which their sidereal periods must be concluded by the method in art. 418.

(539.) It is evident, from a mere inspection of our figure, that the eclipses take place to the west of the planet, when the earth is situated to the west of the line S J, i. e. before the opposition of Jupiter; and to the east, when in the other half of its orbit, or after the opposition. When the earth approaches the opposition, the visual line becomes more and more nearly coincident with the direction of the shadow, and the apparent place where the eclipses happen will be continually nearer and nearer to the body of the planet. When the earth comes to F, a point determined by drawing 6 F to touch the body of the planet, the emersions will cease to be visible, and will thenceforth, up to the time of the opposition, happen behind the disc of the planet. Similarly, from the opposition till the time when the earth arrives at I, a point determined by drawing a I tangent to the eastern limb of Jupiter, the immersions will be concealed from our view. When the earth arrives at G (or H) the immersion (or emersion) will happen at the very edge of the visible disc, and when between G and H (a very small space), the satellites will pass uneclipsed behind the limb of the planet.

(540.) Both the satellites and their shadows are frequently observed to transit or pass across the disc of the planet. When a satellite comes to m, its shadow will be thrown on Jupiter, and will appear to move across it as a black spot till the satellite comes to n. But the satellite itself will not appear to enter on the disc till it comes up to the line drawn from E to the eastern edge of the disc, and will not leave it till it attains a similar line drawn to the western edge. appears then that the shadow will precede the satellite in its progress over the disc before the opposition of Jupiter, and vice versa. In these transits of the satellites, which, with very powerful telescopes, may be observed with great precision, it frequently happens that the satellite itself is

It

discernible on the disc as a bright spot if projected on a dark belt; but occasionally also as a dark spot of smaller dimensions than the shadow. This curious fact (observed by Schroeter and Harding) has led to a conclusion that certain of the satellites have occasionally on their own bodies, or in their atmospheres, obscure spots of great extent. We say of great extent; for the satellites of Jupiter, small as they appear to us, are really bodies of considerable size, as the following comparative table will show:

From which it follows, that the first satellite appears to a spectator on Jupiter, as large as our moon to us; the second and third nearly equal to each other, and of somewhat more than half the apparent diameter of the first, and the fourth about one quarter of that diameter. So seen, they will frequently, of course, eclipse one another, and cause eclipses of the sun (the latter visible, however, only over a very small portion of the planet), and their motions and aspects with respect to each other must offer a perpetual variety and singular and pleasing interest to the inhabitants of their primary.

(541.) Besides the eclipses and the transits of the satellites across the disc, they may also disappear to us when not eclipsed, by passing behind the body of the planet. Thus, when the earth is at E, the immersion of the satellite will be seen at a, and its emersion at b, both to the west of the planet, after which the satellite, still continuing its course in the direction ab, will pass behind the body, and again emerge on the opposite side, after an interval of occultation greater or less according to the distance of the satellite. This interval

Struve, Mem. Art. Soc. iii. 301. † Laplace, Mec. Cel. liv. viii. § 27.