would not fall again to the surface of the moon, but would become a satellite to the earth. Its primitive impulse might, indeed, be such as to cause it even to precipitate to the earth. The stones, which have fallen from the air, may be accounted for in this manner

Satellites of Jupiter.

By the aid of the telescope we may discover four satellites revolving round Jupiter. The sidereal revolutions of these bodies are given in the following table: together with their mean distances from Jupiter, the semi-diameter of that planet's equator being considered as unity; and likewise their masses, compared with Jupiter considered also as unity.

Satellite.

I.

Sidereal Revolution.

Mean
Distance.

Mass.

1d 18h 27′33′′,5 1769137788148 5.812964-0000173281 II. 3 13 13 42,0 3 551181017849 9-248679:0000232355 III. 7 3 42 33,4 7 154552783970 14-752401-0000884972 IV. 16 16 31 49,7 16 68876970708425-946860-0000426591

First Satellite. The inclination of the orbit of this satellite does not differ much from the plane of Jupiter's orbit. Its eccentricity is insensible.

Second Satellite. The eccentricity of the orbit of this satellite is also insensible. The inclination of its orbit, to that of its primary, is variable, as well as the position of its nodes.

Third Satellite. This satellite has a little eccentricity, and the line of its apsides has a direct but variable motion; the eccentricity itself is also subject to very sensible variations. The inclination of its orbit to that of Jupiter, and the position of its nodes, are far from being uniform.

Fourth Satellite. The eccentricity of this satellite is greater than that of any of the other three; and the line of the apsides bas an annual and direct motion of 42′ 58",7. The inclination of its orbit, with the plane of Jupiter's orbit, forms au angle of about 2° 25′ 48′′; but this angle, although stationary about the middle of the last century, has lately begun to increase very sensibly. At the same time the motion of its nodes has begun to diminish.

The motions of the first three satellites are related to each other by a most singular analogy. For, the mean sidereal or synodical

motion of the first, added to twice that of the third, is constantly equal to three times the mean motion of the second. And, the mean sidereal or syno dicallongitude of the first, minus three times that of the second, plus twice that of the third, is always equal to two right angles.

The satellites of Jupiter are liable to be eclipsed by passing through his shadow; and, on the other hand, they are frequently seen to pass over his disk, and eclipse a portion of his surface. This happens to the first and second satellite, at every revolution; the third very rarely escapes in each revolution; but the fourth (on account of its great distance and inclination) is seldom obscured.

These eclipses are of great utility in enabling us to determine the longitude of places, by their observation; and they likewise exhibit some curious phænomena with respect to light.

From the singular analogy, above alluded to, it follows that (for a great number of years at least) the first three satellites cannot be eclipsed at the same time: for in the simultaneous eclipses of the second and third, the first will always be in conjunction with Jupiter, and vice versa.

Satellites of Saturn.

Seven satellites may be seen by means of the telescope, to revolve about Saturn; the elements of which are but little known, on account of their great distance. The following Table will show the duration of their sidereal revolutions, and their mean distances in semi-diameters of Saturn.

The orbits of the first six satellites appear to be in the plane of Saturn's ring; whilst the seventh varies from it very sensibly.»

Satellites of Uranus.

Six satellites revolve round Uranus; which, together with their primary, can be discovered only by the telescope. The following Table will show their sidereal revolutions, and mean distances in semi-diameters of the primary.

All these satellites move in a plane which is nearly perpendi cular to the plane of the planet's orbit, and contrary to the order of the signs!

CHAP. XVII.

[Phil. Mag.]

ON THE DISCOVERY OF THE LAW OF UNIVERSAL
GRAVITATION.

DESCARTES was the first who endeavoured to reduce the mo tions of the heavenly bodies to some mechanical principle. He imagined vortices of subtle matter, in the centre of which he placed these bodies. The vortex of the sun forced the planet into motion; that of the planet, in the same manner, forced its satellite to revolve round it. The motion of comets traversing the heavens in all directions, destroyed these vortices, as they had before destroyed the solid crystalline spheres of the ancient astronomers. Thus, Descartes was no happier in his mechanical, than Ptolemy in his astronomical theory. But their labours have not been useless to science. Ptolemy has transmitted to

us, through fourteen centuries of ignorance, the few astronomical truths which the ancients had discovered. Descartes, born at a later period, and at a time when an universal curiosity was excited, which he himself had increased by substituting, in the place of ancient errors, others more seducing, and resting on the authority of his geometrical discoveries, was enabled to destroy the empire of Aristotle and Ptolemy, which might have stood the attack of a more careful philosopher; but by establishing as a principle, that we should begin by doubting of every thing, he himself warned us to examine his own system with severity, which could not long resist the new truths that were opposed to it. It was reserved for Newton to teach us the general principles of the heavenly motions. Nature not only endowed him with a profound genius, but placed his existence in a most fortunate period. Descartes had changed the face of the mathematical sciences, by the application of algebra to the theory of curves and variable functions. The geometry of infinites, of which this theory contained the germ, began to appear in various places. Wallis, Wren, and Huygens, had developed the laws of motion; the discoveries of Galileo, on falling bodies, and of Huygens on evolutes and centrifugal force, led to the theory of motion in curves; Kepler had determined those described by the planets, and had formed a remote conception of universal gravitàtion; and finally, Hook had distinctly perceived that their motion was the result of a projectile force, combined with the attractive force of the sun. The science of celestial mechanics wanted nothing more to bring it to light, but the genius of a man, who, by generalizing these discoveries, should be capable of perceiving the law of gravitation; it is this which Newton accomplished in his immortal work on the Mathematical Principles of Natural Philosophy. This philosopher, so deservedly celebrated, was born at Woolstrop, in Lincolnshire, towards the latter end of the year 1642, the year in which Galileo died. His first success in his early studies, announced his future reputation; a cursory perusal of elementary books, was sufficient to make him comprehend them; he next read the Geometry of Descartes, the Optics of Kepler, and the Arithmetic of Infinites, by Wallis, but soon aspiring to new inventions, he was, before the age of twenty-seven, in possession of his method of fluxions, and his theory of light. Anxious for repose,

and averse to literary controversy, he delayed publishing his dis coveries. His friend and preceptor, Dr. Barrow, exerted himself in his favour, and obtained for him the situation of professor of mathematics in the university of Cambridge; it was during this period, that, yielding to the request of Halley, and the solicitations of the Royal Society, he published his Principia. The university, of which he was a member, chose him for their representative in the conventional parliament of 1688, and for that which was convened in 1701. He was knighted and appointed director of the mint by Queen Anne; he was elected president of the Royal Society in 1703, which dignity he enjoyed till his death, in 1727. During the whole of his life he obtained the most distinguished consideration, and the nation to whose glory he had so much contributed, decreed him at his death public funeral honours.

In 1666, Newton retired into the country, and, for the first time, directed his thoughts to the system of the world. The descent of heavy bodies, which appears nearly the same at the summit of the highest mountains as at the surface of the earth, suggested to him the idea, that gravity might extend to the moon, and that being combined with some motion of projection, it might cause it to describe its elliptic orbit round the earth. To verify this conjecture, it was necessary to know the law of the diminution of gravity. Newton considered, that if the moon was retained in its orbit by the gravity of the earth, the planets should also be rétained in their orbits by their gravity towards the sun, and demonstrated this by the law of the areas being proportional to the times. Now it results from the relation of the squares of the times to the cubes of the greater axis of their orbits, that their centrifugal force, and consequently their tendency to the sun, diminishes inversely as the squares of the distances from this body. Newton, therefore, transferred to the earth this law of the diminution of the force of gravity, and reasoning from the experiments of falling bodies, he determined the height which the moon, abandoned to itself, would fall in a short interval of time. This height is the versed sine of the arc which it describes in the same interval; and this quantity the lunar parallax gives in parts of the radius of the earth, so that, to compare the law of gravitation with observation, it was necessary to know the magnitude of this radius; but Newton having, at that