286 



CATALOGUE OF POLAR STARS. 



For 3 equidistant intervals a = « + £ [p a + 4/> 2 4- p.^] t = u + P 3 t 



(54) 



For 4 equidistant intervals a = « + £ [p x + 37> 2 + 3jt? 3 + p 4 ~\ t = a + P t t (55) 



For 5 equidistant intervals a = u + ^ s [7 p x + 32^ + 12^> 3 + 3-p t + 7/> 5 ] £ = « + P 5 £ (5G) 



And similarly for 8. 



The values of p t . . . p$ in the application of this method should, in practice, 

 be computed from the co-ordinates derived directly from the observations. If, 

 however, there are not a sufficient number of observations available for the for- 

 mation of the equal intervals, the first three or four values of a derived by the 

 method already described may be used for the computation of the corresponding 

 values of p. 



After this the values of p can be carried forward by differences with suffi- 

 cient accuracy for the computation of the values of a and 8 in advance of the last 



value computed. It will be necessary to carry the reductions for a and 8 along 

 together. 



For the computation of the values p ly p 2 , p^ &c., equations (16) and (20) 



become : 



d a 



dt 



dd 

 dt 



(m + m' t) + {n + n 1 1) sin a tan 5 



(57) 



(n + n' t) cos a 



(58) 



The values of (m ~\- m' t) and log (n -f- n t) can be conveniently written in 



tabular form. The values for intervals of four years from 1875 to 1899 are as 

 follows : 



Epoch, [m + m> t\ [log n + n' t\ log [n -f n/ 1] 



1875 3!b722450 CU2G1147 1.3022060 



1879 3.0723209 0.1261075 1.3021988 



1883 3.0723969 0.1261003 1.3021916 



1887 3.0724729 0.1260931 1.3021844 



1891 3.0725488 0.1260859 1.3021772 



1895 3.0726248 0.1260787 1.3021700 



1899 3.0727008 0.1260715 1.3021628 



&e. &c. &c. 



In illustration of the application of this method of transferring the co-ordinates 

 a and 8 for any epoch f to any epoch tf, we select as provisional values of a and 8 

 those derived by computation from the differential coefficients to the fourth term 

 inclusive, from 1875 to 1899. They are given on page 208. The corresponding 

 values of p ly p 2 , p z , have been computed from equations (57) and (5 





