600 Royal Astronomical Society : — Mr. Main on the 



tinued through the last year to the end of March 1840, and that 

 the most probable values of the parallax resulting from the measured 

 distances of the double star from each of the two stars of compari- 

 son, (a) and {b), are as follo-ws : — 



188 obs. 61-fl.. ..O"-3584-0"-0756A; weight, 64-66 

 214 .. 61 -J -3289— -0276 /t; ... 78-89 



(k being a small indeterminate correction depending on the eiFects 

 of temperature on the micrometer-screw). 



The sums of the squares of the errors cannot, on the supposition 

 of a vanishing yearly parallax, be made less than — 



61— a.'. .12-7282— 3-2445 A;4-0-6330A« 

 61 -b. . . 15-6507-1-6094 A+1-7029 k"- ; 



but on assuming the annual parallax to have the value before as- 

 signed to it, they become — 



61-fl.. 4-4245 -1-0-2579 A 0-2627A:«=4-3614-f-0-2637(;fc-|-0-489)'2 

 ei-J..7-1171-0-1768A-|-l-6426A^=7-1123-|-l-6426(/t-00-54)^ 



On deducing the value of Ic from the observations, those of the 

 first star give, therefore. A: = — 0-489 ; and those of the second 

 k = 0-054. M. Bessel shows that the last of these values is more 

 deserving of confidence than the first ; nevertheless, the true value 

 of the correction is still very doubtful, and it is accordingly left in- 

 determinate. 



Assuming the relative parallax of (a) and (b) to be equal, and 

 having due regard to the mean error of both results, the most pro- 

 bable value of the annual parallax is found 



0"-3483— 0"-0533 k 

 and its mean error +0 -0141. 



This result is greater by 0"-0347 than was found from the first 

 series of observations. 



AssumingA=0, it results from this determination, that the distance 

 of the star 61 Cygni from the sun is 592,200 times the mean radius 

 of the earth's orbit — a distance which light would require 9^ years 

 to pass through. 



He divides the two sets of observations of the distance of 61 Cijgni 

 from the comparison stars (a) and (b), into separate groups, monthly 

 and half.monthly, and takes the mean of the measures in each 

 group as corresponding to the mean of the days in that group. 

 These means are compared with Bessel's mean distances, which he 

 has derived from the solution of his equations, and the chfFerences 

 tabulated. The effect of Bessel's assumed parallax is then com- 

 puted for each mean day, and the resulting numbers placed in an 

 adjacent column. The agreement between the computed effect of 

 parallax and the above-mentioned differences is remarkably close, 

 especially for the measures of distance of the star (a), in which the 

 solution of the equations shows the error of the assumed proper 

 motion to be very small indeed. 



The following are the tabulated monthly groups : — 



