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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 ellipse described by Saturn without being once seen. More 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. 229).
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 excentric 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.
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 Nebulæ Their Number Catalogue of them Consist of Two Classes - Diffuse Nebulæ Definitely formed Nebulæ - Globular Clusters Splendour of Milky Way Nebulæ -The Magellanic Clouds- Nebulæ round tution of Nebulæ, and the Forces that maintain them Shooting Stars.
Distribution of the
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, a Centauri, and Arcturus are the brightest stars in the heavens; the others are classed according to their apparent lustre, from the first to the seventeenth magnitudes. Capella, a Lyræ, Procyon, and twenty or twenty-one more, are of the first magnitude; a Persei, y Orionis, a Cygni, and in all fifty or sixty, are of the second; and of the third there are about 200, such as 7 Bootis and 7 Draconis, the numbers increasing as the magnitude diminishes. Those of the eighth magnitude are scarcely visible to the naked eye, and it requires a very good telescope to see stars of the seventeenth. sequence is perfectly arbitrary; but Sir John Herschel has ascertained by actual measurement the comparative lustre of a great many—for example, he found that the light of a star of the sixth
magnitude is 100 times less than that of one of the first magnitude, and that Sirius would make between three and four hundred of such little stars. Were the photometric scale completed, it would be of the greatest importance with regard to the variable stars.
The three or four brightest classes of stars are scattered pretty equably over the sky, with the exception of a zone or belt following the course of the great eircle passing through € Orionis and a Crucis, where they are very numerous, especially in the southern hemisphere. The stars of all magnitudes visible to the naked eye increase in numbers towards the borders of the Milky Way, which derives its lustre and name from the diffused light of myriads of stars; so numerous are they in some parts of it that more than 50,000 passed through the field of Sir William Herschel's telescope in the course of an hour, in a zone only two degrees broad; in many places they are numerous beyond estimation, and most of them are extremely small on account of their enormous distances.
The Milky Way, which forms so conspicuous a part of the firmament, is a vast and somewhat flattened stratum or congeries of stars, encircling the heavens in a broad band, split through one part of its circumference into two streams of stars, bearing a strong resemblance to fig. 5, plate 5. It is contorted and broken in some places, and occasionally lengthened into branches stretching far into space. Its thickness is small compared with its length and breadth; yet in some places it is unfathomable even with the best telescopes; in others there is reason to believe that it is possible to see through it, and even beyond it, in its own plane. There is a gradual but rapid increase in the crowding of the stars on each side of the flat stratum towards the centre.
The solar system is deeply though excentrically plunged into this mass of stars, near that point where the circular stratum splits into two streams. Sir John Herschel's description of the stars of the southern hemisphere shows that the Milky Way is a most magnificent object there. "The general aspect of the southern circumpolar regions (including in that expression 60° or 70° of south polar distance) is in a high degree rich and magnificent, owing to the superior brilliancy and large development of the Milky Way, which, from the constellation of Orion to
that of Antinous, is a blaze of light, strangely interrupted, however, with vacant and entirely starless patches, especially in Scorpio, near a Centauri and the Cross, while to the north it fades away pale and dim, and is in comparison hardly traceable. I think it is impossible to view this splendid zone, with the astonishingly rich and evenly distributed fringe of stars of the 3rd and 4th magnitude, which forms a broad skirt to its southern border like a vast curtain, without an impression amounting almost to conviction, that the Milky Way is not a mere stratum, but annular, or at least that our system is placed within one of the poorer or almost vacant parts of its general mass, and that eccentrically, so as to be much nearer to the region about the Cross than to that diametrically opposite to it."
Those dark vacuities called "Coal Sacks" by the ancient navigators, which are so numerous between a Centauri and a Antaris, are among the most extraordinary phenomena in the southern hemisphere; they are of intense blackness, though by no means void of extremely small telescopic stars; the darkness arises from the contrast these nearly vacant spaces form with the excessive brillianey of the surrounding part of the Milky Way, and the sudden sharp transition from light to darkness. The largest and most conspicuous of them is a pear-shaped vacuity close to the Southern Cross. That portion of the Milky Way that is split longitudinally through its centre lies between a Centauri and the constellation of Cygnus: the two bands are joined here and there by narrow bridges of condensed stars, stretching across the darker space between them. In Scorpio and Sagittarius Sir John Herschel describes the Milky Way as composed of definite clouds of light running into clusters of extremely minute stars like sand, not strewed evenly as with a sieve, but as if thrown down by handfuls, and by both hands at once, leaving dark intervals. In this astonishing profusion the stars are of all sizes, from the 14th to the 20th magnitude, and even down to nebulosity. After an interval the same profusion is renewed, the stars being inconceivably minute and numerous beyond description-they are in millions and millions. Thus there is great irregularity in their diffusion as well as magnitude -in some places intensely crowded, in others the deep blackness of the sky, over which they are thinly scattered, irresistibly led to believe that in these regions the power of our telescopes fairly