128 



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 Geminorum 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 rotatory motion : 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 <Y Leonis 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 

 different distances affording 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 Herculis afforded a phenomenon hitherto 

 unknown in astronomy ; namely, an occultation of one star by an- 

 other. Whether this be 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 JSeqjentis is calculated at 375 years, and 

 that of y Virginia at 705 years. Their distances have not varied for 



