(on account of the great distance of the earth compared with the radii of the orbits of the satellites) varies but little in the case of each satellite, being nearly equal to the time which the satellite requires to describe an arc of its orbit, equal to the angular diameter of Jupiter as seen from its center, which time, for the several satellites, is as follows: viz., for the first, 2h 20m; for the second, 2h 56m; for the third, 3h 43m; and for the fourth, 4b 56m; the corresponding diameters of the planet as seen from these respective satellites being, 19° 49'; 12° 25'; 7° 47'; and 4° 25'.* Before the opposition of Jupiter, these occultations of the satellites happen after the eclipses: after the opposition (when, for instance, the earth is in the situation K), the occultations take place before the eclipses. It is to be observed that owing to the proximity of the orbits of the first and second satellites to the planet, both the immersion and emersion of either of them can never be observed in any single eclipse, the immersion being concealed by the body, if the planet be past its opposition, the emersion if not yet arrived at it. So also of the occultation. The commencement of the occultation, or the passage of the satellite behind the disc, takes place while obscured by the shadow, before opposition, and its re-emergence after. All these particulars will be easily apparent on mere inspection of the figure (art. 536.). It is only during the short time that the earth is in the arc G H (i.e. between the sun and Jupiter, that the cone of the shadow converging (while that of the visual rays diverges) behind the planet, permits their occultations to be completely observed both at ingress and egress, unobscured, the eclipses being then invisible.

(542.) An extremely singular relation subsists between the mean angular velocities or mean motions (as they are termed) of the three first satellites of Jupiter. 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

These data are taken approximately from Mr. Woolhouse's paper in the supplement to the Nautical Almanack for 1835.

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; and Laplace has demonstrated, that if this relation were at any one epoch approximately true, the mutual attractions of the satellites would, in process of time, render it exactly One curious consequence is, that these three sastellites 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 center, the first must lie on the opposite; and therefore, when at such a conjuncture the first is eclipsed, the other two must lie between the sun and planet, throwing its shadow on the disc, and vice versa.

So.

(543.) Although, however, for the above mentioned reason, the satellites cannot be all eclipsed at once, yet it may happen, and occasionally does so, that all are either eclipsed, occulted, or projected on the body, in which case they are, generally speaking, equally invisible, since it requires an excellent telescope to discern a satellite on the body, except in peculiar circumstances. Instances of the actual observations of Jupiter thus denuded of its usual attendance and offering the appearance of a solitary disc, though rare, have been more than once recorded. The first occasion in which this was noticed was by Molyneux, on November 2d, (old style) 1681.* A similar observation is recorded by Sir W. Herschel as made by him on May 23d, 1802. The phænomenon has also been observed by Mr. Wallis, on April 15th, 1826; (in which case the deprivation continued two whole hours;) and lastly by Mr. H. Griesbach, on September 27th, 1843.

(544.) The discovery of Jupiter's satellites, one of the first fruits of the invention of the telescope, and of Galileo's early and happy idea of directing its new-found powers to the examination of the heavens, forms one of the most

Molyneux, Optics, p. 271.

memorable epochs in the history of astronomy. The first astronomical solution of the great problem of " the longitude" -practically 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 discovery of the aberration of light, and the consequent determination of the enormous velocity of that wonderful element. This we must explain now at large.

(545.) The earth's orbit being concentric with that of Jupiter and interior to it (see fig. art. 536.), 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 26-6 of time allowed. Speculating on the probable physical cause, he was naturally

led to think of a 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. 329.). 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 difference will no doubt be destroyed by nicer and more rigorously reduced observations.

(546.) The orbits of Jupiter's satellites are but little excentric, those of the two interior, indeed, have no perceptible excentricity. Their mutual action produces in them perturbations analagous to those of the planets about the sun, and which have been diligently investigated by Laplace and others. By assiduous observation it has been ascertained that they are subject to marked fluctuations in respect of brightness, and that these fluctuations happen periodically, according to their position with respect to the sun. From this it has been concluded, apparently with reason, that they turn on their axes, like our moon, in periods equal to their respective sidereal revolutions about their primary.

(547.) The satellites of Saturn have been much less studied than those of Jupiter, being far more difficult to observe. The most distant has its orbit materially inclined (no less than 12° 14')* to the plane of the ring, with which the orbits of all the rest nearly coincide. Nor is this the only circumstance which separates it by a marked difference of character from the system of the six interior ones, and renders it in some sort an anomalous member of the Saturnian system. Its distance from the planet's center exceeds in the proportion of nearly three to one that of the most distant of all the rest, being no less than 64 times the radius of the globe of Saturn, a distance from the primary to which our own moon (at 60 radii) offers the only parallel. Its variation of light also in different parts of its orbit is very much greater

Lalande, Astron. Art. 3075.

than in the case of any other secondary planet. Dominic Cassini indeed (its first discoverer, A D. 1671) found it to disappear for nearly half its revolution, when to the east of Saturn, and though the more powerful telescopes now in use enable us to follow it round the whole of its circuit, its diminution of light is so great in the eastern half of its orbit as to render it somewhat difficult to perceive. From this circumstance (viz. from the defalcation of light occurring constantly on the same side of Saturn as seen from the earth, the visual ray from which is never very oblique to the direction in which the sun's light falls on it) it is presumed with much certainty that this satellite revolves on its axis in the exact time of rotation about the primary; as we know to be the case with the moon, and as there is considerable ground for believing to be so with all secondaries.

(548.) The next satellite in order proceeding inwards (the first in order of discovery *) is by far the largest and most conspicuous of all, and is probably not much inferior to Mars in size. It is the only one of the number whose theory and perturbations have been at all enquired into † further than to verify Kepler's law of the periodic times, which holds good, mutatis mutandis, and under the requisite reservations, in this, as in the system of Jupiter. The three next satellites still proceeding inwards are very minute and require pretty powerful telescopes to see them; while the two interior satellites which just skirt the edge of the ring § can only be seen with telescopes of extraordinary power and perfection, and under the most favourable atmospheric circumstances. At the epoch of their discovery they were seen to thread, like beads, the almost infinitely thin fibre of light to which the ring then seen edgeways was reduced, and for a short time to advance off it at either end, speedily to return, and hastening to their habitual concealment behind the body.

• By Huyghens, March 25. 1655.

By Bessel, Astr. Nachr. Nos 193. 214.

Discovered by Dominic Cassini in 1672 and 1684.

§ Discovered by Sir William Herschel in 1789.

An eighth

Considerable confusion prevails in the nomenclature of the Saturnian system, owing to the order of discovery not coinciding with that of distances. Astronomers have not yet agreed whether to call the two interior satellites the