234 



CATALOGUE OF POLAR STARS. 



In like manner, the following values of a and 8 were computed for intervals of 



eight years. 



The places for single years will be easily obtained by successive interpolations 

 to the middle, by means of the formula (see Chauvenet, A^ol. I. p. 88), 



F^ = H^ + F') -\\_h- -r\ K - A LU - &c.)]] 



(9) 



Bessel has given a method (see Wolfers, Tab. Reg., pp. lii, liii) by which the true 

 values of a' and 8' may be computed from an approximate value of a . 

 Let 



«,' = an approximate value of a', 



A< = a< - (3' - ?.'). 



From Napier's first and second Analogies, 



cos 1 {A' + ^) 

 tan ^ (^' - ^) = ^^^ . \2, _ ^) tan ^ 



sin i (A' -V A) 



cotan i ((5' - ^) = -•— f-W, jx tan i d 



- ^ ' sin \ (^4/ — A) 



(10) 

 (11) 



Let the variations in the logarithms of the given functions for a change of 1' 

 have the following designations : 



