48] ON THE MEAN PLACES OF 84 FUNDAMENTAL STARS. 393 



If a denote the K.A. in 1755 and a' the R.A. finally adopted for 

 1845, the R.A. for 1800 will be 



-, 

 p having the same signification as before. 



Similarly, the Declination for 1800 may be found. 



Hence the precession in R.A. for 1800 may be calculated. Let this = c. 

 Then the proper motion in R.A. for the same epoch will be 



90 

 and similar formulae hold for the Declination. 



In consequence of the change of the plane to which the stars are 

 referred, the proper motions in R.A. and Declination will not be strictly 

 uniform, even if the actual proper motions be so. This variability of the 

 proper motion may be very conveniently taken into account in the following 

 manner. 



To the R.A. and Declination for 1845 add the proper motions for 

 45 years just found, and with the places thus obtained calculate the 

 precessions. These combined with the proper motions found for 1800 will 

 give very approximately the annual variations for 1845. 



Similarly, from the R.A. and Declination for 1755 subtract the proper 

 motions for 45 years, and with the places thus obtained calculate the 

 precessions. These combined with the proper motions for 1800 will give 

 very approximately the annual variations for 1755. 



Now let c t be the annual precession calculated in this way for 1755, 

 c that for 1800, and c' that for 1845, and let the differences of these 

 quantities be taken according to the following scheme, 



Ac, 



c A 2 c 



Ac 



c'. 



A. 50 



