Prof. Bessel on the Parallax of the Star 61 Cygni. 71 



necessary to deduce the iveight of the observations contained in the 

 second series, the weight of those in the first series being taken as 

 unit. I have found it =0'68S9; and hence the most probable value 

 of the annual parallax of 61 Cygni =0"'3136. On this hypothesis, 

 I find the mean distances of both stars for the beginning of 1838, to 

 be 46I"'6171 and 706""2791 ; and the corrections of the assumed 

 values of the annual variations, = — 0"-0293 and +0"-2395. The 

 mean error of an observation of the kind of which I have assumed 

 the weight as unit, is + 0""1354, and the mean error of the annual 

 parallax of 61 Cygni, = ± 0"-O202. 



This hypothesis manifestly represents the observations somewhat 

 less correctly than the first calculation which was instituted ; but 

 what we lose in this respect is not sufficient to outweigh the 

 decided preference due to this last calculation. We can form a 

 judgment upon this point by the following lists of errors of the ob- 

 servations, which contain their comparisons with two formulae ; 

 namely, that of the first calculation and the present hypothesis. I 

 have also added a third column, which contains the errors that arise 

 when we assume the parallaxes a" and /3" in the first formula as 

 vanishing. This column also shows immediately what differences 

 were still to be explained by the annual parallax. It shows, in fact, 

 that these differences are commonly positive or negative, accordingly 

 as the coefficient of the annual parallax, which the foregoing tables 

 give, is positive or negative. [The tables here referred to will also 

 be found in the Monthly Notices of the Society, as before.] 



As the mean error of the annual parallax of 61 Cygni (=0"*3136) 

 is only + 0"'0202, and consequently not -Jj of its value computed ; 

 and as these comparisons show that the progress of the influence of 

 the parallax, which the observations indicate, follows the theory as 

 nearly as can be expected considering its smallness, we can no 

 longer doubt that this parallax is sensible. Assuming it 0"'3 136, 

 we find the distance of the star 61 Cygniirom. the sun 657700 mean 

 distances of the earth from the sun: light employs 10'3 years to 

 traverse this distance. As the annual proper motion of a Cygni 

 amounts to 5"" 123 of a great circle, the relative motion of this star 

 and the sun must be considerably more than sixteen semidiameters 

 of the earth's orbit, and the star must have a constant aberration of 

 more than 52''. When we shall have succeeded in determining the 

 elements of the motion of both the stars forming the double star, 

 round their common centre of gravity, we shall be able also to de- 

 termine the sum of their masses. I have attentively considered the 

 preceding observations of the relative positions ; but I consider them 

 as yet very inadequate to afford the elements of the orl)it. I con- 

 sider them sufficient only to show that the annual angular motion is 

 .somewhere about 5 of a degree ; and that the distance, at the be- 

 giiniing of this century, had a mininum of aljout 15". We are enabled 

 hence to conclude that the time of a revolution is more than 540 

 years, and that the semi-major axis of the orbit is seen under an 

 angle of more than 15". If, however, we proceed from these num- 

 bers, which arc merely limits, we find the sum of the masses of both 



