70 Astronomical Society. 



have written against the observations ; we can, therefore, by inspec- 

 tion, perceive how the observations agree with the theory. 



If we compare both divisions of these tables, we shall perceive 

 that the agreement of the observations with each other is consider- 

 ably augmented by giving to a" and ft" positive values ; or, in other 

 words, by admitting a sensible parallax. If we consider this pa- 

 rallax as vanishing, the sum of the squares of the remaining differ- 

 ences of the eightj^-five observations of the star a can be diminished 

 only to 4"4487 ; that of the ninety-eight observations of the star b to 

 4'7I08. If, however, we determine a" and /3", so that the observa- 

 tions may be represented as exactly as possible, we can reduce these 

 sums to r444S and 2'4469. By this means we obtain the mean 

 error of an observation of the star «= + 0"'13'27, of the star b = 

 + 0"'1605. That the observations of the second star are less accu- 

 rate than those of the first, I consider to be owing to the difference 

 of the directions of the two stars with respect to the direction of the 

 double star. The way in which I conceive this difference to affect 

 the result I shall here leave unexplained ; but refer to the complete 

 discussion, which I shall enter into at some future time, of the pa- 

 rallax of 61 Cygni. 



I have employed the preceding list of the observations of the 

 distances of the star 61 Cygni from a and b, in two different ways, 

 in order to deduce from it results for the annual parallax; of a 

 Cygni. I have first assumed o" and /j" as independent of each other ; 

 or, in other words, considered it as not improbable that a and b 

 themselves may possess sensible parallax. In this way I have 

 found. 



For the Star «. 



Mean distance for the beginning of 1838 4Gl"-6094 Mean Error. 



Annual variation =+4"-;5U15-0"-0543 -f'l -3372 +0"0398 



Diflerence of annual parallax of CI and a ... a"=-|-0 -3090 +0 -0283 



For the Star h. 



Mean distance for the beginning of 1838 70f) -2909 



Annual variation = — 2"-825 + 0"-242C -2 -5824 +0 -0434 



Difference of annual parallax of 61 and fi.../3"= -fO -2605 +0 -0278 



The observations seem also to indicate, that the difference of the 

 parallaxes of 61 and b is smaller than that of 61 and a; which must 

 be the case, indeed, if b itself have a sensible parallax greater than a. 

 The difference of the computed values of a" and /3", in fact, exceeds 

 the limits of tlie probalile uncertainty of the observations ; but it is 

 to be observed that the probability of equal values of a'' and fl" is not so 

 small that we should be inclined to consider the difference of the two 

 as j)roved by the observations. Further observations will increase 

 the weight of both results, and, at the same time, give more accu- 

 rate values of the annual variations. 



I have, therefore, deduced a second result from the observations, 

 which rests on the supposition that the parallaxes of a and b arc in- 

 sensible ; or that a" and ft" arc equal. For this purpose, since both 

 series must now be brought into connexion with one another, it was 



