298 CATALOGUE OF POLAR STARS. 



It is obvious from this example, that there is no decided gain in the selection 

 of residuals bejond the order Yo — Y^ for the application of this method, unless 

 the final values Yq — Fj, are chosen. It will be seen that at the end of 15 years 

 after the last date of the series the error amounts to only 0'.06. The computation 

 will be expeditiously performed by making ic = 10, and by changing the equinox 

 at intervals of sixty years. 



Collecting our results, we have, from pages 260, 261, and page 295, for any 

 value of + ^ between 1875 and 1955: 



8. 



a = a„ + [ + 73.514324 + 0.0014106] t 



+ [- 0.15118944 - 0.000033305] fi 

 + [- 0.000339577 + 0.00000093590] t* 

 + [+ 0.00000347-26 - 0.0000000977911]** 

 + [+ 0.0000000089646] t^ 



In like manner, we have from pages 260-264, and from page 296, for any 

 value of —t between 1875 and 1755, t being taken with the position sign in the 

 computation of the secondary terms : 



a = «e + [ + 73^514324 + o!o05808] t 



+ [- 0.15118944 + 0.00064775] fi 



+ [- 0.000339577 + 0.000026536] f 



+ [+ 0.0000034726 + 0.00000050287] t^ 



+ [- 0.000000005169 + 0.0000000043880] «' 



+ [- 0.00000000005554 + 0.000000000014714] t" 



+ 0.0000000000003173 «' 



+ 0.000000000000000163 t^ 



- 0.00000000000000000845 fi 



+ 0.0000000000000000000259 t^" 

 + 0.000000000000000000000119 «" 



- 0.00000000000000000000000080 f 



tli 



The second part of this paper" will be comprised under the following sub- 

 divisions : — 



(«.) Treatment of the proper motion for clo.se polar stars. 



( b.) Yearly ephemerides of all stars within 3° of the pole, between the limits 1860 



and 1885. 

 (c.) Tabular values of the terms U\ W, ?7™, ^7'^ U^, &c., carried as far as will 



be necessary to give the exact reduction for 40 years. 

 {d.) Tabular values of the proper motions at intervals of 8 years for close polar 



stars, and at intervals of 20 years for all other stars. 



