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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 what 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 orb 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. 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 11200000 comets that come within the known extent of our system. 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 Mercury, which makes the number of comets amount to 3529470; but that number may be doubled if it be considered that, in consequence of day-light, fogs, and great southern declination, one comet out of two is concealed from us. So, according to M. Arago, more than seven millions of comets frequent the planetary orbits.
Great as the number of comets appears to be, it is absolutely nothing when compared to the number of the fixed About two thousand only are visible to the naked eye; but when we view the heavens with a telescope, their number seems to be limited only by the imperfection of the instrument. In one hour Sir William Herschel estimated that 50000 stars passed through the field of his telescope, in a zone of the heavens 2o in breadth. This, however, was stated as an instance of extraordinary crowding; but at an average, the whole expanse of the heavens must exhibit about a hundred millions of fixed stars that come within the reach of telescopic vision.
The stars are classed according to their apparent brightness, and the places of the most remarkable of those visible to the naked eye are ascertained with great precision, and formed into a catalogue, not only for the determination of geographical position by their occultations, but to serve as points of reference for finding the places of comets and other celestial phenomena. The whole number of stars registered amounts to about 15000 or 20000. The distance of the fixed stars is too great to admit of their exhibiting a sensible disc: but, in all probability, they are spherical, and must certainly be so if gravitation pervades all space, which it may be presumed to do, since John Herschel has shown that it extends to the binary systems of stars. With a fine telescope the stars appear like a point of light, their occultations by the moon are therefore instantaneous; their twinkling arises from sudden changes in the refractive power of the air, which would not be sensi
ble if they had discs like the planets. Thus we can learn nothing of the relative distances of the stars from us and from one another by their apparent diameters; but their annual parallax being insensible, shows that we must be one hundred millions of millions of miles at least from the nearest; many of them, however, must be vastly more remote, for of two stars that appear close together, one may be far beyond the other in the depth of space. The light of Sirius, according to the observations of Sir John Herschel, is 324 times greater than that of a star of the sixth magnitude; if we suppose the two to be really of the same size, their distances from us must be in the ratio of 57-3 to 1, because light diminishes as the square of the distance of the luminous body increases.
Nothing is known of the absolute magnitude of the fixed stars, but the quantity of light emitted by many of them shows that they must be much larger than the sun. Dr. Wollaston determined the approximate ratio that the light of a wax candle bears to that of the sun, moon, and stars, by comparing their respective images, reflected from small glass globes filled with mercury, whence a comparison was established between the quantities of light emitted by the celestial bodies themselves. By this method he found that the light of the sun is about twenty millions of millions of times greater than that of Sirius, the brightest, and supposed to be the nearest of the fixed stars. If Sirius had a parallax of half a second, its distance from the earth would be 525481 times the distance of the sun from the earth; and therefore Sirius, placed where the sun is, would appear to us to be 3.7 times as large as the sun, and would give 13.8 times more light; but many of the fixed stars must be infinitely larger than Sirius.
Many stars have vanished from the heavens; the star 42 Virginis seems to be of this number, having been missed by Sir John Herschel on the 9th of May, 1828, and not again found, though he frequently had occasion to observe that part of the heavens. Sometimes stars have all at once appeared, shone with a bright light, and vanished. Several instances of these temporary stars are on record; a remarkable instance occurred in the year 125, which is said to have induced Hipparchus to form the first catalogue of stars. Another star appeared suddenly near a Aquila in the year 389, which vanished after remaining for three weeks as bright as Venus. On the 10th of October, 1604, a brilliant star burst forth in the constellation of Serpentarius, which continued visible for a year; and a more recent case occurred in the year 1670, when a new star was discovered in the head of the Swan, which, after becoming invisible, reappeared, and after many vari ations in light vanished after two years, and has never since been seen. In 1572, a star was discovered in Cassiopeia, which rapidly increased in brightness till it even surpassed that of Jupiter; it then gradually diminished in splendour, and after exhibiting all the variety of tints that indicates the changes of combustion, vanished sixteen months after its discovery without altering its posi tion. It is impossible to imagine anything more tremendous than a conflagration that could be visible at such a distance. It is however suspected that this star may be periodical and identical with the stars which appeared in the years 945 and 1264. There are probably many stars which alternately vanish and reappear among the innumerable multitudes that spangle the heavens, the periods of thirteen have already been pretty well ascertained.
Of these the most remarkable is the star Omicron in the constellation Cetus. It appears about twelve times in eleven years, and is of variable brightness, sometimes appearing like a star of the second magnitude; but it neither always arrives at the same lustre, nor does it increase or diminish by the same degrees. According to Hevelius,
it did not appear at all for four years. y Hydræ also vanishes and reappears every 494 days, and a very singular instance of periodicity is given by Sir John Herschel in the star Algol or ẞ Persei, which is described as retaining the size of a star of the second magnitude for two days and fourteen seconds; it then suddenly begins to diminish in splendor, and in about three hours and a half is reduced to the size of a star of the fourth magnitude; it then begins again to increase, and in three hours and a half more regains its usual brightness, going through all these vicissitudes in two days, twenty hours, and forty-eight minutes. The cause of the variations in most of the periodical stars is unknown, but, from the changes of Algol, M. Goodricke has conjectured that they may be occasioned by the revolution of some opaque body, coming between us and the star, obstructing part of its light. Sir John Herschel is struck with the high degree of activity evinced by these changes in regions where, but for such evidences, we might conclude all to be lifeless.' He observes that our own sun requires nine times the period of Algol to perform a revolution on its own axis; while, on the other hand, the periodic time of an opaque revolving body sufficiently large to produce a similar temporary obscuration of the sun, seen from a fixed star, would be less than fourteen hours.
Many thousands of stars that seem to be only brilliant