Royal Astronomical Society. 391 



In the instance of ij Coronse there is a difficulty of a totally dif- 

 ferent kind. The two stars are so very nearly equal in magnitude 

 and similar in colour, that, when observations are interrupted for a 

 long time, it is impossible to say whether that which is adopted as 

 the zero- star before and after the interruption is the same ; and it 

 is therefore necessary in some cases to make double computations, 

 on the two suppositions that the first star, or the second star, is 

 that to which the measures are referred in other observations. 



From the observations to which they had access, M. Struve, Sir 

 John Herschel, and M. Madler, concluded that the periodic time of 

 this star was 43 or 44 years, M, Villarceau, however, has had 

 access to the observations made at Pulkowa from 1826 up to 1847, 

 and has treated them in the following manner : — 



Of fifteen observations, four were rejected, on account of 

 manifest errors in the distance only. From the remaining eleven, 

 relations were obtained between the elements, which leave them 

 dependent upon an indeterminate quantity which is arbitrary be- 

 tween very wide limits. The observations of Sir John Herschel 

 in 1823, and of M. Struve from 1826 to 1847, may be represented 

 with sufficient accuracy by ellipses in which the periodic time 

 ranges from 38 to 190 years. To fix this indeterminate quantity, 

 we may take Sir W. Herschel's observation of 1781 or that of 1802 

 (with a slight alteration sanctioned by Sir John Herschel). If we 

 fix the indeterminate quantity by the observation of 1802, M. Vil- 

 larceau finds that the observation of 1781 is also satisfied, provided 

 that the position of the stars be reversed ; that is, provided that it 

 be assumed that the other star has been used as the zero, which is 

 perfectly admissible. Thus is obtained an orbit with a periodic 

 time of 66 years. 



But if we reverse the position of the stars in 1802, which is 

 admissible, it is found that the observation of 1781 is satisfied 

 without reversion. The periodic time thus obtained is 43 years. 



It is remarkable that in these totally different solutions the 

 excentricity is sensibly the same, namely, 0"47. 



In both cases the remaining errors are so small, in comparison 

 with the probable errors, as to leave the two solutions equally 

 entitled to our reception. For the final judgement between them, 

 M. Villarceau refers to some remarks of Sir W. Herschel, unac- 

 companied by measures. Although there is some doubt in the 

 interpretation of these, M. Villarceau thinks that upon the whole 

 the solution which gives a period of QQ years is the more probable. 

 He remarks, however, that in four years at the furthest the doubt 

 will be settled. In 1853'677 the angle of position given by the 

 66-year solution will be 303° 44', while that given by the 43-year 

 solution will be 356° 30', leaving a difference upon which there can 

 be no doubt. The distances will be respectively 0"*51 and 0"*77, 

 but between these it might be difficult to pronounce. 



