CATALOGUE OF POLAR STARS. 235 



A log cos \ (.4/ ^- A) — c /i log sill J {A^ - A) = s' 



/I log cos 4- (^1/ - ^) = c' J log tan I (tV - 5) = < 



d log sin I (^j' + ^1) = 5 z/ log tan J (pi + ijj = c/ 



d = the value of J ((5' — tt) oLtained fioiu equation (10) 

 d' = " " i {S' + S) " " " (11) 



X = the lequiicd correction to a/ in order to obtain u' 



^ ~ t ' ~ t< 



Then 



a - ((?' - d) 



a' = «,' + X. (12) 



5' = d' + d + (j^ + y) X. (13) 



Tills method may be conveniently applied when we have a series of values of a 

 and require any following term of the series. From the differences of the given 

 values of a an approximation to the true value may be obtained, from which the 

 correction x can be computed. The exact values of a and S' will then be deter- 

 mined from equations (12) and (13) respectively. 



Let us assume that the values of a have been found for 1875, 1883, and 1891 

 as follows : 



o / // 



5= +88 59 37.C9 



Assuming the second difference, -20«.201, as a constant, we obtain, for 1899, 



fi. in, a. 



«/ = 7 TiG r)9.874 



To find the true d for 1899, we have 



