great enough to render it visible; and that it remains invisible while the plane of the ring lies between the earth and the sun, because, then, the dark side is turned towards us. The same Cassini discovered that the ring is divided by a dark elliptical line into two parts which are concentric with each other, but of unequal brilliancy, and he first observed the lines, or belts, which are commonly seen on the surface of the planet. Jaques Cassini, his son, remarking that the disappearance and re-appearance of the two sides of the ring do not take place, respectively, after equal intervals of time, concluded that the whole surface of the ring is not exactly, in one plane; and M. Messier, in 1773, from the inequalities of the light as well as from the appearance of distinct luminous points when the breadth of the ring was very much diminished, concluded that the surface is considerably diversified with mountains and valleys. The shadow cast by the planet itself on the plane of the ring had been early observed; but Sir William Herschell was the first who perceived the shadow cast by the ring on the body of the planet, at a time when the edge of the former, being turned towards the earth, was itself, invisible.

Huygens was fortunate enough to discover one of the satellites of Saturn; but, misled by the spirit of system, he rashly committed himself by asserting that there remained no more satellites to discover because their number was, then, exactly equal to the number of primary planets. Dominicus Cassini subsequently discovered that Saturn was accompanied by four other satellites; and, among the first discoveries made by Herschell with the great telescope he had constructed, was that of two more, which made the whole number equal to seven.

The phenomena of the planets were particularly attended to by Dominicus Cassini, and his discoveries contributed materially to establish the opinion that all the solar system is subject to one law of action; his observations on the spots of Mars and Jupiter enabled him to decide that they adhere to those planets, and, appearing larger when near the centre than elsewhere, it was evident that they revolve with the planets about the axes of the latter; and the times of their appearance and disappearance, and the positions of the paths they describe, shewed the periods in

which the revolutions are performed and the inclinations of the axes to the planes of the orbits. The same astronomer determined, also, the dimensions and positions of the orbits of Jupiter's satellites; and, from his observations of their movements, he was enabled to compute the times at which they appear, to the inhabitants of the earth, to become eclipsed by entering into the shadow of the planet: he foresaw the importance of these phenomena in the solution of the problem for finding the longitudes of places on the earth; but, before they could be rendered available for this purpose, a far more accurate knowledge of the movements of the satellites was required. In 1677, Cassini remarked a spot on the body of Jupiter, at a time when the fourth satellite was known to be between the earth and planet, and he observed that the spot quitted the latter at the moment the satellite became visible: it was, therefore, evident that this was the satellite itself, rendered visible only by the superior brilliancy of the planet. Now this appearance was not found to occur every time that the satellite was on the planet, but only after intervals of twelve years; and the inference drawn from the circumstance was that the satellites of Jupiter, like our moon, revolve on their axes in the times of their revolutions about the planet; by which means the same face of the satellite is turned towards the earth at the end of every revolution of Jupiter about the sun, and is rendered visible to us from the diminution of its brilliancy, caused by the spots supposed to be on its surface. The same astronomer, observing that the fifth satellite of Saturn gradually lost and recovered its brilliancy during its movement through the eastern and western parts of its orbit, respectively, inferred that the same law prevailed in the rotations of the satellites of that planet; an inference which was subsequently confirmed by Herschell. By one part of the disc of Venus appearing less bright than the rest, Cassini was enabled to follow that planet in its rotation on its axis; and he, from thence, concluded the time in which the rotation was performed, but with some hesitation because, on account of her apparent vicinity to the sun, she is not visible during a sufficient length of time. M. Schroeter has, however, since, confirmed the opinion of Cassini from his observations on the returns of like appearances at

one of the cusps of that planet. Her movement of rotation was found to be directed nearly from north to south, a circumstance in which she is distinguished from the other planets, whose rotations are nearly from west to east, and which indicates a very small obliquity of her axis to the plane of her orbit. Another phenomenon observed by Dominicus Cassini was, that the dise of Jupiter is not circular but elliptical, being in a sensible degree compressed at the poles; his instruments were, however, not sufficiently good to allow him to ascertain the difference between the two diameters, but this was afterwards accomplished by Pound and Short, in England: a similar compression has been, subsequently, observed in the other planets, and that of Saturn is particularly great.

The librations of the moon had been observed before the time of Cassini and that by which we, occasionally, see an additional portion of the upper and lower edge of the disc had been rightly ascribed to the position of the spectator, who looks down upon her when she is in the horizon, and under her when she is near the meridian; but the above astronomer appears to have been the first who ascribed the libration in longitude to a difference between her velocity in the orbit and that of the rotation on her axis.

Besides numerous observations tending to the discovery of the forms of the planets and to a more correct determination of their mean movements by a comparison of the ancient with the modern places, the enquiries of astronomers were, in the same age, particularly directed to those circumstances which relate to the positions of the planetary orbits themselves; such as their obliquity to the ecliptic and the motions of their nodes and aphelia, which had been, in former times, very incorrectly ascertained. Maraldi determined, by means of an observation made in the year 300 Before Christ, the position of the ascending node of Jupiter's orbit, and comparing it with the position of the same node, observed 1934 years subsequently, he found that, in the interval, it had advanced 12 degrees with respect to the equinoctial points; but these having, in the same time, retrograded 27 degrees, it was evident that the node must have retrograded, with respect to the fixed stars, as much as 14 degrees. The

same astronomer, and his relative, Jacques Cassini, suspected, also, that the aphelia of the orbits of Jupiter and Saturn had, each, a progressive motion in space because, in the course of ages, they appeared to have advanced more than the equinoctial points had retrograded; but the want of precision in the observations did not allow them to conclude positively that such was the fact. The same uncertainty, then, prevailed concerning the movements of the nodes of Mercury and Venus, which La Hire and Cassini supposed to be in retrograde order.

The mean motions of the planets were, in this age, ascertained very correctly by comparisons of the actual places with those determined from the observations of Tycho Brahe and of the ancient astronomers; but Maraldi and Cassini discovered the remarkable fact, that the mean motion of Jupiter was, then, more rapid, and that of Saturn, less so than they had formerly been this circumstance, which is, now, so well known to be caused by the mutual perturbations exercised by those planets on each other, appeared at first to be quite inexplicable: the latter astronomer, however, proposed an opinion that the effects resulted, in some manner, from the changes which take place in the positions of the orbits, in consequence of the progression of their apsides; and, with singular good fortune, he conjectured that the time would come when those effects would be of a contrary nature; the motion of Saturn becoming more rapid than that of Jupiter, and so on, alternately. La Lande, also, in the middle of the eighteenth century, ascertained from observation, that, during about thirty-five years previously, the mean motion of Saturn had experienced an abrupt acceleration; and the discovery of the cause of these inequalities of movement was, soon afterward, to follow. Several variations were, also, at this time, found to take place in the movements of Jupiter's satellites, in the inclinations of their orbits and in the positions of the apsides and nodes. The nodes of the fourth satellite were found to move in direct, instead of retrograde order; and those of the second, to have a motion which is alternately direct and retrograde.

CHAPTER XX.

THE THEORY OF GRAVITATION DEVELOPED BY NEWTON.

Huygens measures the intensity of terrestrial attraction by the vibrations of pendulums. Dr. Hook's illustration of planetary motion.-Newton discovers that terrestrial gravity extends beyond the moon.— on.-He demonstrates the laws of planetary motion—Manner in which a planet describes an elliptical orbit.—Universality of the principle of attraction. The sun and planets revolve about the centres of gravity. The planets disturb each other's motions.-- The perturbations produce movements in the apsides and nodes of an orbit.-Manner of decomposing a perturbating force.- Effects of perturbation in changing the figure of a planet's orbit.—Application of the theory of attraction to the moon.-Causes of the several inequalities in the moon's motions.-Cause of the retrogradation of the equinoctial points. - Physical cause of the tides.-Cause that the moon always presents the same face to the earth.--The comets shewn to be subject to the law of gravitation.-Objections at first urged against Newton's theory.-Newton's preference of the geometrical mode of investigating propositions.

ABOUT the middle of the seventeenth century Huygens, in Holland, discovered the laws by which a body descends and ascends along the arc of a cycloid, and his attempt to produce a movement of this nature, in the pendulum applied to machinery for the purpose of measuring time, in order to render the vibrations isochronous, is well known; but, though this ingenious project was not attended with the success at first anticipated, yet the laws of motion in a cycloid were found to be of great importance in the determination of the relations between the times of motion and the spaces passed through, by bodies descending near the earth, from the force of terrestrial attraction; and became the means of obtaining an expression for the intensity of that kind of attraction.

Galileo had proved, mathematically, that, since gravity is a force continually acting, it must cause a falling body to descend through spaces proportional to the squares of the times of descent; and attempts had been, subsequently, made to verify the proposition by letting bodies fall from the tops of buildings to the ground,