positions, to exhibit phases like the moon; but no such appearance has been detected, except in one instance, when they are said to have been observed by Hevelius and La Hire, in the year 1682. In general, the light of comets is dull-that of the comet of 1811 was only equal to the tenth part of the light of the full moon-yet some have been brilliant enough to be visible in full daylight, especially the comet of 1744, which was seen without a telescope at one o'clock in the afternoon, while the sun was shining. Hence it may be inferred that, although some comets may be altogether diaphanous, others seem to possess a solid mass resembling a planet. But whether they shine by their own or by reflected light has never been satisfactorily made out till now. Even if the light of a comet were polarized, it would not afford a decisive test, since a body is capable of reflecting light, though it shines by its own. M. Arago, however, has, with great ingenuity, discovered a method of ascertaining this point, independent both of phases and polarization.

Since the rays of light diverge from a luminous point, they will be scattered over a greater space as the distance increases, so that the intensity of the light on a screen two feet from the object is four times less than at the distance of one foot; three feet from the object, it is nine times less, and so on, decreasing in intensity as the squares of the distances increase. As a self-luminous surface consists of an infinite number of luminous points, it is clear that, the greater the extent of surface, the more intense will be the light; whence it may be concluded that the illuminating power of such a surface is proportional to its extent, and decreases inversely as the squares of the distances. Notwithstanding this, a self-luminous surface, plane or curved, viewed through a hole in a plate of metal, is of the same brilliancy at all possible distances as long as it subtends a sensible angle, because, as the distance increases, a greater portion comes into view; and, as the augmentation of surface is as the square

of the diameter of the part seen through the whole, it increases as the squares of the distances. Hence, though the number of rays from any one point of the surface which pass through the hole decreases inversely as the squares of the distances, yet, as the extent of surface which comes into view increases also in that ratio, the brightness of the object is the same to the eye as long as it has a sensible diameter. For example -Uranus is about nineteen times farther from the sun than we are, so that the sun, seen from that planet, must appear like a star with a diameter of a hundred seconds, and must have the same brilliancy to the inhabitants that he would have to us if viewed through a small circular hole having a diameter of a hundred seconds. For it is obvious that light comes from every point of the sun's surface to Uranus, whereas a very small portion of his disc is visible through the hole; so that extent of surface exactly compensates distance. Since, then, the visibility of a self-luminous object does not depend upon the angle it subtends as long as it is of sensible magnitude, if a comet shines by its own light, it should retain its brilliancy as long as its diameter is of a sensible magnitude; and, even after it has lost an apparent diameter, it ought to be visible, like the fixed stars, and should only vanish in consequence of extreme remoteness. That, however, is far from being the case-comets gradually become dim as their distance increases, and vanish merely from loss of light, while they still retain a sensible diameter, which is proved by observations made the evening before they disappear. It may therefore be concluded, that comets shine by reflecting the sun's light. The most brilliant comets have hitherto ceased to be visible when about five times as far from the sun as we are. Most of the comets that have been visible from the earth have their perihelia within the orbit of Mars, because they are invisible when as distant as the orbit of Saturn: on that account there is not one on record whose perihelion is situate beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last appearance, remained five whole years within the

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ellipse described by Saturn without being once seen. than a hundred and forty comets have appeared within the earth's orbit during the last century that have not again been seen. If a thousand years be allowed as the average period of each, it may be computed, by the theory of probabilities, that the whole number which range within the earth's orbit must be 1400; but, Uranus being about nineteen times more distant, there may be no less than 11,200,000 comets that come within the orbit of Uranus. M. Arago makes a different estimate: he considers that, as thirty comets are known to have their perihelion distance within the orbit of Mercury, if it be assumed that comets are uniformly distributed in space, the number having their perihelion within the orbit of Uranus must be to thirty as the cube of the radius of the orbit of Uranus to the cube of the radius of the orbit of Mercury, which makes the number of comets amount to 3,529,470. But that number may be doubled, if it be considered that, in consequence of daylight, fogs, and great southern declination, one comet out of two must be hid from us. According to M. Arago, more than seven millions of comets come within the orbit of Uranus.

The different degrees of velocity with which the planets and comets were originally propelled in space is the sole cause of the diversity in the form of their orbits, which depends only upon the mutual relation between the projectile force and the sun's attraction.

When the two forces are exactly equal to one another, circular motion is produced; when the ratio of the projectile to the central force is exactly that of 1 to the square root of 2, the motion is parabolic; any ratio between these two will cause a body to move in an ellipse, and any ratio greater than that of 1 to the square root of 2 will produce hyperbolic motion (N. 222).

The celestial bodies might move in any one of these four curves by the law of gravitation: but, as one particular velocity is necessary to produce either circular or parabolic

motion, such motions can hardly be supposed to exist in the solar system, where the bodies are liable to such mutual disturbances as would infallibly change the ratio of the forces, and cause them to move in ellipses in the first case, and hyperbolas in the other. On the contrary, since every ratio between equality and that of 1 to the square root of 2 will produce elliptical motion, it is found in the solar system in all its varieties, from that which is nearly circular to such as borders on the parabolic from excessive ellipticity. On this depends the stability of the system; the mutual disturbances only cause the orbits to become more or less eccentric without changing their nature.

For the same reason the bodies of the solar system might have moved in an infinite variety of hyperbolas, since any ratio of the forces, greater than that which causes parabolic motion, will make a body move in one of these curves. Hyperbolic motion is however very rare; only two comets appear to move in orbits of that nature, those of 1771 and 1824; probably all such comets have already come to their perihelia, and consequently will never return.

The ratio of the forces which fixed the nature of the celestial orbits is thus easily explained; but the circumstances which determined these ratios, which caused some bodies to move nearly in circles and others to wander towards the limits of the solar attraction, and which made all the heavenly bodies to rotate and revolve in the same direction, must have had their origin in the primeval state of things; but, as it pleases the Supreme Intelligence to employ gravitation alone in the maintenance of this fair system, it may be presumed to have presided at its creation.

SECTION XXXVII.

The Fixed Stars-Their Number-The Milky Way-Double Stars-Binary Systems-Their Orbits and Periodic Times-Colours of the Stars-Stars that have vanished-Variable Stars-Variation in Sun's Light-Parallax and Distances of the Fixed Stars-Masses of the Stars-Comparative Light of the Stars-Proper Motions of the Stars-Apparent Motions of the Stars -Motion and Velocity of the Sun and Solar System-The Nebula-Their Number-Catalogue of them-Consist of Two Classes-Diffuse Nebulæ― Definitely formed Nebula-Globular Clusters-Splendour of Milky Way -Distribution of the Nebula-The Magellanic Clouds-Nebulæ round Argûs-Constitution of Nebulæ, and the Forces that maintain them— Meteorites and Shooting Stars.

GREAT as the number of comets appears to be, it is absolutely nothing in comparison of the multitude of the fixed stars. About 2000 only are visible to the naked eye; but, when the heavens are viewed through a telescope, their number seems to be limited only by the imperfection of the instrument. The number registered amounts to 200,000, their places are determined with great precision, and they are formed into a catalogue, not only for the purpose of ascertaining geographical positions by the occultations of the brightest among them, but also to serve as points of reference for marking the places of comets and other celestial phenomena. Sirius, Rigel, Aldebaran, &c., are of the first magnitude; those of the eighth magnitude are scarcely visible to the naked eye, and it requires a very good telescope to show those of the 17th.

The stars are scattered very irregularly over the sky; in some places they are thinly dispersed, in others crowded together, especially in the Milky Way, which derives its brightness from the diffused light of myriads of stars: so numerous are they in some parts of it that more than