Each of these hypotheses having been carefully investigated. it is
found that all except that of a rotatory motion of the small star round
the large one, or of their joint motions round a common centre of
gravity, offer difficulties which cannot be surmounted. Adopting,
therefore, this last-mentioned hypothesis as the true one, our author
proceeds to a more detailed examination of the several angles of
position he has taken in the course of his observations; and having
also determined those angles by calculation from the annual rate of
56' 18", deduced from the total change in the whole period, he finds
the agreement so obvious as hardly to admit of a doubt of this being
the true mode of accounting for these variations. He has, moreover,
the satisfaction of being able to quote an observation of Dr. Bradley,
made in the year 1759, which he lately obtained from Dr. Maskelyne ;
according to which, the two stars of a Geminor'um were in that year
seen in an angular position, exactly corresponding with the situation
they ought to have been in, according to the rate here assigned for
their rotatorymotion: so that the time of a periodical revolution may
now be calculated from an arch of 45° 30', which has been described
in forty-three years and a half.
Thus, from the great regularity of this motion, he now thinks him- self authorized to conclude, that the orbit in which the small star moves _round the large one, or perhaps the orbits in which they both move round their common centre of gravity, are nearly circular, and at right angles to the line in which we see them; and that the time of a'whole apparent revolution will be about 342 years 10 months.
We shall not presume to enter here upon any detail of the inves- tigations respecting the five other double stars mentioned in this paper, any further than to record the general results deduced from them.
In vyLeonis the plane of the orbit of the small star is found not to be at right angles with the line of vision, the distances having varied considerably since the commencement of the observations, and these difierent distances afi'ording the elements of an ellipsis which will explain the appearances, although the orbit be in fact, or nearly, cir— cular. The periodical time of this revolution is calculated at about 1673 years.
As to E Bootis, the changes observed during twenty-two years in- dicate that one of the periodical revolutions cannot take up much less than 1681 years; but as the figure and situation of the orbit cannot as yet be accurately determined, some uncertainty still re- mains even concerning this period.
The observations_on g Herculis afforded a phaenomenon hitherto unknown in astronomy; namely, an occultation of one star by an- other. Whether this he owing to solar parallax, to proper motion, or to the motion of one of the stars in an orbit whose plane is nearly coincident with the visual ray, is not as yet determined; nor is any periodical time hitherto assigned to it.
The periodical time of 8 Serpentis is calculated at 375 years, and that of 7 Virginis at 705 years. Their distances have not varied for
