402 Ow the apparent Place of the Pole- Star. 



whence, the mean places, for the 1st of January in the years 

 1820, 182!, and 1822, will be as under: viz. 



A\. in time. D. 



1820= 0". 57'. 0",r)S3 88°. 20'. 54",609 



1821= 57. 15,20y 21. 14 ,055 



1822= 57. 29,909 21. 33 ,495 



c , 



Next come the corrections on accoinit of precession, aberra- 

 tion, nutation occ: and it is here that M. Bessel has shown that 

 peculiar talent for analysis, for which he is so jnstlv celebrated. 

 The formulae for these corrections are thrown into a synoptical 

 table, in page 404, for the sake of a more convenient rtference; 

 and are taken from the fourth part of the Astrcnomicai ol)serva- 

 tions made by M. Bessel at the Royal Oljservatory in Konigs- 

 berg; a work which contains a fund of useful and interesting in- 

 formation, and is by far the best specimen of an active observa- 

 tory, of any extant. The quantities, expressed by A\, D, co, ©, 

 }) , £3 , denote respectively the right ascension and declination 

 of the star, the obliquity of the ecliptic, the true longitude of the 

 sun, the true longitude of the moon, and the place of the moon's 

 nodes. 



In the formulae No. 2 and 5, the reader will readily recognise 

 the common formulae for aberration and nutation : the co-efficients 

 for the nutation are those given by M. Lindenau ; and for the 

 aberration, that adopted by M.Delambre. The other quantities 

 are here for the first time deduced by M. Bessel, for the purpose 

 of determining the apparent place of the star to the greatest ex- 

 actness. By the help of a few subsidiary tables he has rendered 

 the use of these fnrmulfe very simple and easy. The formulae 

 1. 2. 3. 4 he has thrown together into one table, showing their 

 values for every fifth day of the year: 5. 6. 7, together with the 

 mean place of the star, he has thrown together into another table, 

 showing their vahies for every hundredth day, for the years 1805 

 to 182(3: No. S. 10 are in separate tables : and 9 is altogether 

 omitted, as its maximum never exceeds 0",01 . These subsidiary 

 tables are c- Icniatef! for the meridian of Paris, and corrections are 

 given for applvir.g them to the meridians of other observatories: 

 the correction for Greenwich is insensible. 



From tliese subsidiary tables, the following tables have been cal- 

 culated: and it should l)c particularly observed that they show the 

 apparent place ot the pole-star at (he time of its upper culmi- 

 nation; and not its place a/ 7Won, from which it will frequently 

 very sensibly differ. M. Bessel has explained the method, 

 wtierebv he deduces the apparent place of a star at the time of 

 its culmination, in Bode's Jlstronomisches Jahrbuch for 1817, 

 page 197; as well as in his Fundavienta Aslronomice, page 67, 



where 



