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of parallax, an arc of 1' is assumed as the parallactic unit. Now radius is to the sine of 1" as 206,265 is to 1; hence, a Centauri is 206,265 times more distant from the sun than the sun is from the earth. Light flying at the rate of 192,000 miles in a second must take 3 years and 83 days to come to us from that
One or two tenths of a second becomes a very great error when the maximum amount of parallax is only 1", and on that account, with the exception of a Centauri, it has been found impracticable to determine the annual changes in the apparent motions of single stars affected by precession, nutation, aberration, and the variations of temperature of the instruments used in observing. However, as two stars in juxtaposition are equally affected by all of these, the difference in their motions is independent of them. Of two stars apparently in close approximation, one may be far behind the other in space. They may seem near to one another when viewed from the earth in one part of its orbit, but may separate widely when seen from the earth in another position, just as two terrestrial objects appear to be one when viewed in the same straight line, but separate as the observer changes his position. In this case the stars would not have real, but only apparent motion. One of them would seem to oscillate annually to and fro in a straight line on each side of the other, a motion that could not be mistaken for that of a binary system where one star describes an ellipse about the other; or if the edge of the orbit be turned towards the earth, where the oscillations require years for their accomplishment. The only circumstances that can affect the stars unequally, and which must be eliminated, are the proper motion of the stars in space, and specific aberration, a very minute quantity arising from peculiarities in the star's light. This method of finding the distances of the fixed stars was proposed by Galileo and attempted by Dr. Long without success. Sir William Herschel afterwards applied it to some of the binary groups; and although he did not find the thing he sought for, it led to the discovery of the orbital motions of the double stars.
M. Struve was the first to apply this method, and that in a very difficult case. He perceived that a very small star is close to a Lyræ, and by a series of most accurate differential measurements from 1835 to 1838 he found that a Lyræ has a parallax of 0"-261, which was afterwards corroborated by the observations of
M. Peters; hence a Lyræ is 789,600 times more distant from the sun than the earth is.
It was natural to suppose that in general the large stars are nearer to the earth than the small ones; but there is now reason to believe that some stars, though by no means brilliant, are nearer to us than others which shine with greater splendour. This is inferred from the comparative velocity of their proper motions; all the stars have a general motion of translation, which tends ultimately to mix those of the different constellations; but none that we know of moves so rapidly as 61 Cygni, and on that account it was reckoned to be nearer to us than any other, for an object seems to move more quickly the nearer it is. Now M. Bessel saw that two minute and probably very remote stars are very near 61 Cygni, their directions from that star being at right angles to one another; so that, during the revolution of the earth, one of these distances was a maximum and the other a minimum alternately every three months. This alternation, although it indicated a parallax or difference of parallaxes of only 0" 348, was maintained with such perfect regularity every three months, that it leaves not a doubt of its accuracy, which was afterwards confirmed by the observations of M. Peters at Polkova. It follows from that small parallax that 61 Cygni must be 592,700 times farther from the earth than the sun isa distance that light would not pass over in less than nine years and three months.
Mr. Henderson found the parallax of Sirius, the brightest of all the stars, to be only 0"-230; it is consequently more distant than 61 Cygni, though the latter is but of the 6th magnitude.
M. Argelander has calculated that the apparent magnitude of the stars depends upon their distance. Supposing them all to be of the same size, the smallest visible in Sir William Herschel's 20 feet reflecting telescope, namely those of the 17th magnitude, would be 228 times farther off than those of the first magnitude; and M. Peters of Polkova from the annual parallax of thirty-five, seven of which are now very accurately determined, has ascertained the distance of the nearest of them to be such, that light flying at the rate of 95 millions of miles in a second would take 15 years and a half to come from them to the earth, and that a star of the 17th magnitude might be extinguished for 3541 years before we should be aware of it. (N. 231.)
The great gulfs that separate the stars from the sun, and probably from one another, no doubt maintain the stability of the stellar system, in the same manner that in the solar system the distances of the planets from the sun and the satellites from their primaries are so arranged as to preserve their mutual disturbances within due limits. The stars supposed to be nearest the sun are probably in a great zone which crosses the Milky Way between n Argûs and a Crucis. η It comprises the bright stars of the constellations Orion, Canis Major, the Southern Cross, Centaur, Lupus, and Scorpio. The axis of the zone is inclined at an angle of 20° to the medial line, or circle, passing through the centre of the Milky Way.
A very great number of stars undergo periodical changes of lustre, varying in some cases from complete extinction to their original brilliancy, strongly suggesting the idea that they are temporarily obscured, and sometimes completely hid, by opaque bodies revolving round them in regular periodic times, as the planets do about the sun.
The star Mira, or o Ceti, which was first noticed to be periodical by Fabricius, in 1596, appears about twelve times in eleven years, or in periods of 331d 8h 4m 16; it remains at its greatest brightness about a fortnight, being then on some occasions equal to a large star of the second magnitude; then it decreases during about three months, till it becomes completely invisible to the naked eye, in which state it remains about five months; after that it continues increasing during the remainder of its period. Such is the general course of its changes; but it does not always return to the same degree of brightness, nor increase and diminish by the same gradations, neither are the successive intervals of its maxima equal. From the observations and investigations of M. Argelander, the mean period given is subject to fluctuation, embracing 88 such periods, and having the effect of gradually lengthening and shortening alternately those intervals to the extent of 25 days one way and the other. The irregularities in the degree of brightness attained at the maximum are probably also periodical. For four years previous to 1676 it did not appear at all; and on October 5, 1839, it exceeded a Ceti, and equalled B Auriga, in lustre. These irregularities may be occasioned by periodical perturbations among opaque bodies revolving about the star. Algol, or B Persei, is another very remarkable
instance of a variable star. It has the size of a star of the second magnitude for two days and thirteen and a half hours, and then suddenly begins to diminish in splendour, till, in about three hours and a half, it 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 brightness, going through all these vicissitudes in 2d 20h 48m 548.7. Sir John Herschel and Mr. Goodricke, by whom the variable nature of this star was discovered in 1782, considered this to be a case strongly indicative of the revolution of an opaque body, which, coming between us and Algol, cuts off a large portion of the light. This star has been constantly observed, and the more recent observations, compared with the ancient ones, indicated a diminution in the periodic time. It is even proved that this decrease is not uniformly progressive, but is actually proceeding with accelerated rapidity, which, however, will probably not continue, but will by degrees relax, and then be changed into increase, according to the laws of periodicity, which, as well as their causes, remain to be discovered. The first minimum of this star, in 1844, happened on January 3rd, at 4b 14m Greenwich time. y Hydræ also vanishes and reappears every 494 days. B Lyra was discovered to be variable, in 1784, by Mr. Goodricke, and its period was ascertained by Argelander to be 12d 21h 53m 10, in which time a double maximum and minimum takes place, the two maxima being nearly equal, but the two minima unequal; besides these semi-periods, there is a slow aberration of period, which appears to be periodical itself: from its discovery to 1840 the time was continually lengthening, but more and more slowly, till, in 1840, it ceased to increase, and has since been slowly on the decrease.
The stars & Cephei and ŋ Aquila, or Antinoi, were discovered to be variable in 1784; their respective periods, being 5d 8h 47m 39o and 7d 4h 13m 53°, have since been accurately determined. Besides these, the variations of between 30 and 40 have been approximately ascertained, and a great many more among the smaller stars have been discovered to be variable by Mr. Hind, who has remarked that many of those stars which continue visible at their minimum appear hazy and indistinct, as though some cloudy or nebulous medium intervened. Some of the variable stars are red, and others present successive changes through blue, yellow, and red. When the brightness is increasing the star has a blueish tinge,
when it is past its maximum lustre it assumes a yellow tint, and while on its decrease it becomes ruddy with flashes of bright red light. These changes are very marked in a small star near the star 77, at the extremity of the south wing of Virgo.
Sir John Herschel, after having described the glory of the starry heavens, asks, “For what purpose are we to suppose such magnificent bodies scattered through the abyss of space? Surely not to illuminate our nights, which an additional moon of the thousandth part the size of our own would do much better, nor to sparkle as a pageant void of meaning and reality, and bewilder us with vain conjectures. Useful, it is true, they are to man as points of exact and permanent reference; but he must have studied astronomy to little purpose who can suppose man to be the only object of his Creator's care, or who does not see in the vast and wonderful apparatus around us provision for other races of animated beings. The planets, we have seen, derive their light from the sun, but that cannot be the case with the stars. These doubtless then are themselves suns, and may perhaps, each in its sphere, be the presiding centre round which other planets or bodies, of which we can form no conception from any analogy offered by our own system, may be circulating."
Another circumstance shows how probable it is that dark bodies are revolving among the stars. The proper motion of Sirius is very irregular-sometimes it is rapid, and at other times slow; the cause is ascribed by MM. Bessel and Peters to a dark companion which revolves with Sirius about their common centre of gravity, and by its attraction disturbs the equable motion of the star.
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 one 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 on the 11th of November, 1572, a star all at once shone forth in Cassiopeia, which rapidly increased in brightness till it surpassed that of Jupiter so much as to be visible at midday. It began to decrease in December of