CATALOGUE OF TOLAR STARS, 



235 



A log cos \ {A I + A) 



c 



A log cos \ {AJ 



^ 



c 



I 



d log sin $ (A{ + A) 



s 



/J log sin I (A/ 

 zf log tan \ (cV 



-/. 



i) 



«) 



J log tan J (d' + J) 



/ 



< 



*' 



tf 



d' 



x 



P 



the value of \ (d f - 8) obtained from equation (10) 



u 



u 



i (5' + 5) 



u 



.. 



u 



(11) 



the required correction to a/ in order to obtain a 



/ 



i(o 



c>) 



t 



7 



H* 



5') 



*' 



Then 



a; 



rt 



(* 



<0 



r -fl 



«' = « ' + a;. 



(12) 



3 



/ 



<7' + J + (p + j') x. 



(13) 



This 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 



o 



and (13) respectively. 



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



as follows: 





h. 771. $. 



1875 7 29 5.G31 



1883 



1891 



7 38 43.913 



7 48 1.994 



Ai 



+ 9 38.232 



+ 9 18.081 



o / 



/' 



A, 



8 



+ 88 59 37.G9 



9. 



20.201 



Assuming the second difference, -20v2ol, as a constant, we obtain, for 1899, 



h. m. 



s. 



t 



a L ' = 7 56 59.874 



To find the true a for 1899, we have 



