298 



CATALOGUE OF POLAR STAES. 



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

 of residuals beyond the order Y — Y 3 for the application of this method, unless 

 the final values Y Q — Y 12 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 S .06. The computation 

 will be expeditiously performed by making w = 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 + t between 1875 and 1955: 



s. 



a = a + [ + 73.514324 + 0.0014106] t 



+ [- 0.15118944 - 0.000033305] t 2 

 + [- 0.000339577 + 0.00000093590] t 9 

 + [+ 0.0000034726 - 0.0000000977911] t* 



+ [ + 0.0000000089646] t 5 



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: 



O 



« = « + [ + 73.514324 + 0.005808] t 



+ [- 0.15118944 + 0.00064775] t 2 

 + [- 0.000339577 + 0.000020536] f 

 + [+ 0.0000034726 + 0.00000050287] t* 

 + [- 0.000000005169 + 0.0000000043880] t 5 

 + [- 0.00000000005554 + 0.000000000014714] t 

 + 0.0000000000003173 V 

 + 0.000000000000000163 t» 



0.00000000000000000845 fi 

 + 0.0000000000000000000259 < 10 

 + 0.000000000000000000000119 t n 

 0.00000000000000000000000080 t™ 



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



divisions : 



(a.) Treatment of the proper motion for close 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 1 , U n , U m , U 1Y , V y , &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. 



