recently published by the Astronomical Society of London. 341 



and the natural numbers, corresponding to the sums of those 

 logarithms, will give the whole correction, either in right 

 ascension or declination, as may be required ; and with a de- 

 gree of accuracy not previously attempted. 



" The mode by which this great saving of time and labour 

 is obtained, has been, in some measure, already explained by 

 me in the Philosophical Magazine for October 1822; and the 

 plan, which was first published by Professor Bessel, has been 

 partially acted on by Professor Schumacher in his Astrono- 

 mische Hiilfstafeln for the same year. The tables of M. Schu- 

 macher, however, comprehend little more than two-thirds of 

 the first class, only, of the stars to which I am about to al- 

 lude ; and do not exceed five hundred in number. 



" The stars, which form the subject of the present tables, 

 consist of the three following classes : 



" 1°. All the stars, to the fifth magnitude inclusive, where- 

 soever situated. 



" 2°. All the stars, to the sixth magnitude inclusive, si- 

 tuated within 30° of the equator. 



" 3°. All the stars, to the seventh magnitude inclusive, si- 

 tuated within 10° of the ecliptic. 



" This selection, it is presumed, will form one of the most 

 useful catalogues for practical astronomy that can well be sug- 

 gested. It contains all the stars of the above description, 

 which have been observed (with sufficient accuracy for deter- 

 mining their present positions) by Flamsteed, Bradley, La 

 Caille, Mayer, Piazzi, and Zach." 



Mr. Baily then proceeds to explain the mode by which the 

 stars have been brought up by precession ; and likwise the 

 method of forming the general tables of precession, aberration, 

 and nutation : illustrating the same by suitable examples. 



When the catalogue was finished, it became desirable to 

 ascertain how far the mean places of the stars (which had 

 been brought up from the observations of Bradley and Piazzi 

 by means of the proposed formula) could be depended upon. 

 With this view a comparison was made with the places of the 

 36 Greenwich stars that have been observed and reduced at 

 different times by Messrs. Bessel, Brinkley, and Pond: and 

 which is inserted at the end of the work. 



There are two Catalogues of the Right Ascension of the 

 36 Greenwich stars published by M. Bessel in the Konigsberg 

 Observations : one (which may be considered as Dr. Maske- 

 lyne's catalogue of 1805) redi *>! to 1815, and the other (de- 

 pending on M. Bessel's own ooservations) reduced to 1825. 

 Both these catalogues were brought up to 1830 by means of 



the 



