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as we are.
after it has lost an apparent diameter, it ought, like the fixed stars, to be visible, 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
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 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 Uranus to 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 stars. 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 Sir 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 sensible if they had discs like the planets. Thus we can learn nothing of the rela
tive 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 in
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 Aquilæ 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 variations