48] ON THE MEAN PLACES OF 84 FUNDAMENTAL STAES. 391 



order to refer the R.A. to the most probable position of the Equinox as 

 determined from the observations of the whole 12 years, the RA. for 1840 

 must be increased by 8- 028 and those for 1845 diminished by the same 

 quantity. 



The mean epoch of the observations on which the Catalogue for 1840 

 depends is the beginning of 1839, and the observations may be looked upon 

 as giving the places for that time, independently of any assumed proper 

 motion. The proper motions for 1 year should therefore be added to the 

 places for 1840 of those stars whose proper motions have not been taken 

 into account, and to the places of the other stars should be added, for the 

 sake of uniformity, 



Adopted proper motion for 1 year Proper motion employed in the reductions. 



The proper motions employed may be those given in the Fundamental 

 Catalogue in the Nautical Almanac for 1848, which are those of Argelander 

 as far as he gives them, the rest being taken from the B. A. Catalogue. 



The proper motions used by the Astronomer Royal in his reductions 

 are those given in the Nautical Almanac for 1834. For two stars, proper 

 motions are mentioned in the notes to the Catalogue of 1439 stars, which 

 are not given in the Nautical Almanac, viz. for a Aquilce, a proper motion 

 of 0"'32 in N.P. D., and for t Piscium, a proper motion of + O s- 025 in 

 R.A., both being taken from Baily. These however are not included in 

 the Annual Precessions of that Catalogue, and I am not quite certain that 

 they have been used in obtaining the places for 1840. The Astronomer 

 Royal should be consulted on this point. 



The R.A. for 1755 given in the Fundamenta should be diminished by 

 8 '020 in consequence of Bessel having employed too large a value of the 

 coefficient of nutation in his reductions. 



The next step is to reduce the places for 1840 to the epoch 1845. 



If a denote the R.A. for 1755, a, that for 1840, and half the secular 

 variation of the precession in R.A. be denoted by p, as in the Nautical 

 Almanac Catalogue, then the R.A. for 1845 will be 



a, a 9 

 a ' + ~l^ + 2 P > 

 and similarly for the Declination. 



The value of p may be taken at once from the Nautical Almanac for 

 1848. The value there given, however, does not include the small terms 



