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This circumstance furnishes the means of finding the absolute breadth of the orbit in miles, and from that the true distance of the star from the earth. For, since the greatest and least distances of the satellite star from the earth differ by the breadth of its orbit, the time which the star takes to move from the nearest to the remotest point of its orbit is greater than it ought to be by the whole time its light takes to cross the orbit, and the period of moving through the other half is exactly as much less. Hence the difference between the observed times of these two semirevolutions of the star is equal to twice the time that its light employs to cross its orbit; and, as we know the velocity of light, the diameter of the orbit may be found in miles, and from that its whole dimensions; for the position of the orbit with regard to us is known by observation, as well as the place, inclination, and apparent magnitude of its major axis, or, which is the same thing, the angle under which it is seen from the earth. Since, then, three things are known in this great triangle, namely, the base or major axis of the orbit in miles, the angle opposite to it at the earth, and the angle it makes with the visual ray, the distance of the satellite star from the earth may be found by the most simple of calculations. The merit of having first proposed this very ingenious method of finding the distance of the stars is due to M. Savary; but, unfortunately, it is not of general application, as it depends upon the position of the orbit, and a long time must elapse before observation can furnish data, since the shortest period of any revolving star that we know of is 30 years. Still the distances of a vast number of stars may ultimately be made out in this way; and, as one important discovery almost always leads to another, their masses may thus be weighed against that of the earth or sun.
The only data employed for finding the mass of the earth, as compared with that of the sun, are, the angular motion of our globe round the sun in a second of time, and the distance of the earth from the sun in miles (N. 233). Now, by observations of the binary systems, we know the angular velocity of the small star round the great one; and, when we know the distance between the two stars in miles, it will be easy to compute how many miles the small star would fall through by the attraction of the great one in a second of time. A comparison of this space with the space through which the earth would descend towards
the sun in a second will give the ratio of the mass of the great star to that of the sun or earth. According to M. Bessel, the weight of the two stars of 61 Cygni is equal to half the weight of the sun. Little as we know of the absolute magnitude of the fixed stars, 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 which 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 a Lyræ is five and a half times greater than that of the sun. Sir John Herschel reflected the moon's light totally by a prism, which, concentrated by a lens, was compared directly with that of a Centauri. After making allowance for the quantity of the moon's light lost in passing through the lens and prism, he found that the mean quantity of light sent to the earth by a full moon exceeds that sent by a Centauri in the proportion of 27,408 to 1. Now, Dr. Wollaston found the proportion of the sun's light to that of the full moon to be that of 801,072 to 1. Hence, the light sent to us by the sun is to that sent by a Centauri as about twentytwo thousand millions to one. But, as the parallax of a Centauri is 1", it really is two and a half times brighter than the sun. The light of Sirius is four times that of a Centauri, but its parallax is only 0" 230: hence it has an intrinsic splendour 63.02 times that of our luminary. It is therefore estimated to be a hundred times as large; so that, were Sirius in the earth's place, its surface would extend 150 times as far as the orbit of the moon. 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.
So many of the stars have proper motions altogether independent of the annual rotation of the earth in its orbit, that it may be doubted whether there be such a thing as a fixed star. Groombridge is the most rapid known: it has a proper motion of 7" of arc annually; « Centauri moves at the rate of 3′58 annu
ally, and 61 Cygni describes a line in space of 5" 12 in the same time. These motions are probably in curves, but at the distance of the earth they will appear to be rectilineal for ages to come. The motion of little more than five seconds of space, which 61 Cygni describes annually, seems to us to be extremely small; but at the distance of that star an angle of one second corresponds to twenty-four millions of millions of miles; consequently the annual motion of 61 Cygni is 120 millions of millions of miles, and yet, as M. Arago observes, we call it a fixed star. From the same cause it is evident that the crowding of the stars in the Milky Way may be apparent only, and that the stars may be at vast distances from one another, and no doubt are.
Were the solar system and the whole of the stars visible to us carried forward in space by a motion common to all, like ships drifting in a current, it would be impossible for us, moving with the rest, to ascertain its direction. Sir William Herschel perceived that a great part of the motions of the stars is only apparent, arising from a real motion of the sun in a contrary direction. Among many discrepancies he found that the stars in the northern hemisphere have a general tendency to move towards a point diametrically opposite to a Herculis, which he attributed to a motion of the solar system in a contrary direction. For it was evident to him, that the stars, from the effects of perspective alone, would seem to diverge in the direction to which the solar system was going, and would converge towards the space it had left, and that there would be a regularity in these apparent motions which would hereafter be detected. Since Sir William Herschel's time the proper motions of the stars have been determined with much greater accuracy, and many have been added to the list by comparing the ancient and modern tables of their places; his views have been established by four of the greatest astronomers of the age, MM. Lundahles, Argelander, Otto Struve, and Peters, who have clearly proved the motion of the sun from that of the stars in the northern hemisphere, and Mr. Galloway has come to the same conclusion from the motions of the stars in the southern hemisphere (N. 234). The result is, that the sun, accompanied by all his attendant planets, is moving at the rate of 422,424 miles-or over a space nearly equal to his own diameter-in the course of a day, and that the motion is
directed towards a point in a line joining the two stars and Herculis at a quarter of the apparent distance of these two stars, reckoning from Herculis. This investigation was founded upon no law assumed or observed, such as the circulation of all the stars of our firmament about a common centre, though philosophers have speculated as to the probability of such a motion in the sun and stars in the plane of the Milky Way. Should the sun and his stellar companions be moving in a nearly circular orbit, the centre of motion would be in the plane passing through the sun perpendicular to the direction of his motion. The constellations through which that great circle would pass are Pisces, Australis, Pegasus, Andromeda, Perseus, &c. M. Argelander is of opinion that the sun's orbit is nearly in the plane of the Milky Way, and, therefore, that its centre must probably be in Perseus, while M. Mädler places it in the Pleiades, which seems to be inadmissible; but the data are too uncertain at present to admit of any absolute conclusion as to the sun's orbit and the general motion of the stellar firmament: for though the stars in every region of the sky tend towards a point in Hercules, it is not yet known whether their motions are uniform or variable, whether the sun's motion be gradually changing, and whether the stars form different independent systems, each having its own centre of attraction, or if all obey one powerful controlling force which pervades the whole universe. Accurate observations of the places of a select number of stars of all dimensions in the Milky Way continued for a series of years would no doubt decide this point.
The proper motion of a star combined with the progressive velocity of light alters the apparent periodic time of the revolving star of a binary system. If the orbit of a double star be at right angles to the visual ray, and both the sun and the star at rest, the periodic time of the revolving star, say of 10,000 days, would always be the same. But if the centre of gravity of the star were to recede in a direct line from the sun with the velocity of one tenth of the radius of the earth's orbit in a day, then at the end of 10,000 days it would be more remote from us by 1000 of such radii-a space light would take 57 days to traverse: hence, although the periodic time of the star would really be the same, the completion of its period would only be known to us 57 days after it had taken place, so that the periodic time would
appear to us to be 10,057 days instead of 10,000. Were the star to approach to the sun by the same quantity instead of receding, the apparent periodic time would be diminished by 57 days.
As the sun is only a unit in the stellar system, so the Milky Way, and all the stars that adorn the firmament of both hemispheres, constitute a group which is but a unit among the infinite numbers of starry clusters and nebula that are profusely scattered throughout the universe.
By the aid of a good telescope there may be seen on the clear vault of heaven, between the stars of our own stellar system, and far in the depths of space, an immense multitude of objects like comets or clouds of white vapour of all forms and sizes. Some are mixed with stars, others are entirely formed of them. Many appear as if they were stellar, but required a telescope of higher power to resolve them, and vast numbers appear to be matter rarefied in the highest possible degree, giving no indication of a stellar nature; and these are in every state of condensation, from a vague film hardly to be discerned to such as have actually arrived at a solid nucleus of stars. The cloudy appearance is merely the blending of the rays of innumerable stars which are themselves invisible from their extreme distance, like parts of the Milky Way. Sir William Herschel was at first of that opinion, and the nebula that have been resolved by Lord Rosse's telescope have led astronomers to believe that such is the case. Yet the tails of comets, the zodiacal light, and the extensive luminous atmospheres which encompass many of the stars, show that, in all probability, a self-luminous phosphorescent material substance in a highly diluted or gaseous form exists in vast abundance.
The number of the nebulæ, like that of the stars, is only limited by the imperfection of our instruments, for each improvement in the telescope only enables us to penetrate a little farther into the infinity of space-to see a few more of these shadowy existences in the far distance, and to resolve a few more of those that are comparatively near. Sir William Herschel examined the nature and determined the position of 2500 nebulæ in the northern hemisphere whose places were computed from his observations, reduced to a common epoch, and arranged into a catalogue, in order of right ascension, by his sister, Miss Caroline Herschel, who added lustre to the name she bore by her eminence in astronomical knowledge and discovery. Sir John Herschel revised