42] ROYAL ASTRONOMICAL SOCIETY TO M. PETERS. 313 



M. Busch has deduced the constant of nutation from Bradley 's obser- 

 vations at Kew and Wansted. The reductions are made in the most 

 strict manner, except that the annual parallaxes are neglected, and M. Peters 

 regards the result as worthy of the highest confidence. 



M. Peters then enters upon his own investigations, which are based 

 on 603 right ascensions of Polaris, observed at Dorpat between 1822 and 

 1838, with Reichenbach and Ertel's meridian circle. Of these observations, 

 the first 249 were made by M. Struve, and the remaining 354 by M. Preuss. 

 These are compared with the right ascensions deduced from the Tabula 

 Regiomontance, and the equations of condition thence arising are treated 

 by the method of least squares, taking as the unknown quantities the 

 correction of the constant of nutation, the correction of the constant of 

 aberration, the annual parallax, the corrections for the position of the axis 

 of the transit-circle (illuminated pivot east or west), the correction of the 

 star's right ascension, and the personal equation of the two observers. 



The equations are first solved, giving equal weight to all the obser- 

 vations. The observations are then divided into two groups (one for each 

 observer), and the equations of each group are solved separately. There 

 is a surprising agreement between the results found from the four years' 

 observations of M. Struve, and the twelve years' observations of M. Preuss, 

 the coefficients of nutation deduced differing by less than three-hundredths 

 of a second. This investigation supplies a measure of the precision of the 

 separate observations, and it is found that M. Struve's observations are 

 entitled to greater weight than those of M. Preuss. 



The whole of the observations are then combined, giving the proper 



relative weights just obtained, and the equations are re-solved. The values 



found for the unknown quantities differ extremely little from the results 

 given by the supposition of equal weights. 



One of the most striking results is the constant difference between 

 the right ascension given by the two observers, or the personal equation, 

 which amounts, for Polaris, to more than 0'8 of a second of time. The 

 magnitude of this shews that the personal equation changes with the 

 declination of the stars. Hence, also, we may easily understand that 

 M. Lindenau's results may be vitiated by the omission of the consideration 

 of personal equation, especially as the observations which he employed were 

 made with different instruments, as well as by different observers. 



A. 40 



