394 ON THE MEAN PLACES OF 84 FUNDAMENTAL STARS. [48 



Then one-half the secular variation of precession for 1850, 



10 f* , n , 



or p = - r XAC + --A-C 



Annual rate of variation for 1850, 



, a' -a 127 



or K = 



a! and a being as before the R. A. for 1845 and 1755 respectively. 

 Also, R.A. for 1850, 



Similar formula, of course, hold for the Declination. 



If the difference between the determinations for 1845 exceed 8 '05 for 

 R. A. or l" for Declination, it should be ascertained whether the places 

 have been rightly derived from those given in the several volumes of the 

 Greenwich Observations. I found, for instance, a discrepancy in the R.A. 

 of a Ceti, and on examination it appeared that the R. A. for 1840 should 

 be 2 h 53 m 55 9 '23 instead of 2 h 53 m 55 8 '32 ; the correction -0 9 '09 mentioned 

 in the Introduction to the Catalogue having apparently been omitted. 



The calculation of the Fundamental places should be carried to 3 places 

 of decimals in R.A., and 2 in Declination, and the calculation of the 

 Precessions and Secular Variations should be carried to 5 places in R.A. 

 and 4 in Declination. 



I may mention here that the Secular Variations of Precession given in 

 the British Association Catalogue do not include the terms which depend 

 on the variation of m and n. Also that for Bradley's Stars the proper 

 motions are calculated by using Bessel's old values of the precession given 

 in the Funaamenta, and therefore ought not to be combined with the 

 annual precessions given in the same Catalogue, which are founded on his 

 later elements. Consequently, with the Precessions, Secular Variations, and 

 proper motions of the Catalogue, we cannot reproduce the places for 1755, 

 which were taken as the basis of calculation. 



