speaking, its eclipses happen, like those of the rest, each revolution.

(460.) 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.

(461.) Suppose S to be the sun, E the earth in its orbit EFG K, J Jupiter, and ab 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 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 from 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 some

what 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 SJ 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. 353. (note.)

(462.) 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 SJ, 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 b F to touch the body of the planet, the emersions will cease to be visible, and will thenceforth, to an equal distance on the other side of the opposition, happen behind the disc of the planet. 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.

(463.) When the 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. It appears then that the shadow will precede the satellite in its progress over the disc before the opposition, and vice versâ. 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 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.*

(464.) An extremely singular relation subsists between the mean angular velocities or mean motions (as they are termed) of the three first satellites of Jupiter. + Laplace, Mec. Col. liv. viii. § 27.

* Struve, Mem. Ast. Soc. iii. 301.

If the mean angular velocity of the first satellite be added to twice that of the third, the sum will equal three times that of the second. From this relation it follows, that if from the mean longitude of the first added to twice that of the third, be subducted three times that of the second, the remainder will always be the same, or constant, and observation informs us that this constant is 180°, or two right angles; so that, the situations of any two of them being given, that of the third may be found. It has been attempted to account for this remarkable fact, on the theory of gravity by their mutual action. One curious consequence is, that these three satellites cannot be all eclipsed at once; for, in consequence of the last-mentioned relation, when the second and third lie in the same direction from the centre, the first must lie on the opposite; and therefore, when the first is eclipsed, the other two must lie between the sun and planet, throwing its shadow on the disc, and vice versa. One instance only (so far as we are aware) is on record when Jupiter has been seen without satellites; viz. by Molyneux, Nov. 2. (old style) 1681.*

(465.) The discovery of Jupiter's satellites by Galileo, one of the first-fruits of the invention of the telescope, forms one of the most memorable epochs in the history of astronomy. The first astronomical solution of the great problem of "the longitude" the most important for the interests of mankind which has ever been brought under the dominion of strict scientific principles, dates immediately from their discovery. The final and conclusive establishment of the Copernican system of astronomy may also be considered as referable to the discovery and study of this exquisite miniature system, in which the laws of the planetary motions, as ascertained by Kepler, and especially that which connects their periods and distances, were speedily traced, and found to be satisfactorily maintained. And (as if to accumulate historical interest on this point) it is to the observation of their eclipses that we owe the grand dis* Molyneux, Optics, p. 271.

covery of the aberration of light, and the consequent determination of the enormous velocity of that wonderful element. This we must explain now at large.

(466.) The earth's orbit being concentric with that of Jupiter and interior to it (see fig. art. 460.), their mutual distance is continually varying, the variation extending from the sum to the difference of the radii of the two orbits, and the difference of the greater and least distances being equal to a diameter of the earth's orbit. Now, it was observed by Roemer, (a Danish astronomer, in 1675,) on comparing together observations of eclipses of the satellites during many successive years, that the eclipses at and about the opposition of Jupiter (or its nearest point to the earth) took place too soon-sooner, that is, than, by calculation from an average, he expected them; whereas those which happened when the earth was in the part of its orbit most remote from Jupiter were always too late. Connecting the observed error in their computed times with the variation of distance, he concluded, that, to make the calculation on an average period correspond with fact, an allowance in respect of time behoved to be made proportional to the excess or defect of Jupiter's distance from the earth above or below its average amount, and such that a difference of distance of one diameter of the earth's orbit should correspond to 16m 26s-6 of time allowed. Speculating on the probable physical cause, he was naturally led to think of the gradual instead of an instantaneous propagation of light. This explained every particular of the observed phenomenon, but the velocity required (192000 miles per second) was so great as to startle many, and, at all events, to require confirmation. This has been afforded since, and of the most unequivocal kind, by Bradley's discovery of the aberration of light (art. 275.). The velocity of light deduced from this last phænomenon differs by less than one eightieth of its amount from that calculated from the eclipses, and even this differ