4. Being able thus to discern, in distant regions of the universe, bodies revolving about each other, we have the means of determining, as we do in our own solar system, the masses of the bodies so revolving. But for this purpose, we must know their distance from each other; which is, to our vision, exceedingly small, requiring, as we have said, high magnifying powers to make it visible at all. And again, to know what linear distance this small visible distance represents, we must know the distance of the stars from us, which is, for every star, as we know, immensely great; and for most, we are destitute of all means of determining how great it is. There are, however, some of these binary systems, in which astronomers conceive that they have sufficiently ascertained the value of both these elements, (the distance of the two stars from each other, and from us,) to enable them to proceed with the calculation of which I have spoken; the determination of the masses of the revolving bodies. In the case of the star _Alpha Centauri_, the first star in the constellation of the Centaur, the period is reckoned to be 77 years; and as, by the same calculator, the apparent semi-axis of the orbit described is stated at 15 seconds of space, while the annual parallax of each star is about one second, it is evident that the orbit must have a radius about 15 times the radius of the earth's orbit; that is, an orbit greater than that of Saturn, and approaching to that of Uranus. In the solar system, a revolution in such an orbit would occupy a time greater than that of Saturn, which is 30 years, and less than that of Uranus, which is about 80 years: it would, in fact, be about 58 years. And since, in the binary star, the period is greater than this, namely 77 years, the attraction which holds together its two elements must be less than that which holds together the Sun and a planet at the same distance; and therefore the masses of the two stars together are considerably less than the mass of our sun. 5. A like conclusion is derived from another of these conspicuous double stars, namely, the one termed by astronomers _61 Cygni_; of which the annual parallax has lately been ascertained to be one-third of a second of space, while the distance of the two stars is 15 seconds. Here therefore we have an orbit 45 times the size of the Earth's orbit; larger than that of the newly-discovered planet Neptune, whose orbit is 30 times as large as the earth's, and his period nearly 165 years. The period of 61 Cygni is however, it appears, probably not short of 500 years; and hence it is calculated that the sum of the masses of the two stars which make up this pair is about one-third of the mass of our Sun.[4]