CATALOGUE OP POLAR STARS. 



247 



It will be found convenient to represent the entire coefficients of (? 



'of, (f 



t ) 4 , &c, in equations (14) and (15) by a single expression. 



>o), if 



tof, 



Let 



U 1 



U n 



ipn 



pry 



da 





dt 





1 d 2 a 





2 dt* 





1 d s a 





2.3 dt 3 





1 d* 



a 



2.3.4 dt 4 



&c., 



Then writing t for 



and 



) we have 



W 



i 



W u 



w 



III 



w 



IV 



dt 



i (P_s 



J_ d*d 

 2.3 </« 8 



1 



d 4 8 



2.3.4 c7« 4 



&c. 



a 



5 



« + £7^ + Z7 n « 2 + Z7 m « 8 + U lv t A ,&c. 

 d + WH+ W n t* + W m t? + W IV t\ &c. 



(48) 

 (49) 



We now compute the right ascension of Groombridge 1119 for / 

 120, corresponding to the years 1855, 1835, 1795, and 1755. 

 With the data 



20 



40 



80, 



da 

 dt 



s. 



+ 73.514324 



f7 2 a 



dt 



2 



S. 



.30237888 



d*a 



dt s 



S. 



.0020374621 



d*a 

 dt* 



8. 



+ .00008334240 



and the values of 



IP 



8. 



73.514324 



IP 1 



8. 



.15118944 



S. 



.000339577 



ipv 



s. 



+ .0000034726 



we have, 



a 



o 



U 1 t 



U n t 2 



IP 11 ? 

 U^t 4 



+ 

 + 



For 1855. 



h 771. s, 



7 29 5.6310 



24 30.2865 



1 0.4758 



2.7166 



0.5556 



a 



7 3 38.1409 



For 1835. 



h. m. s. 



7 29 5.6310 

 49 0.5730 

 4 1.9031 

 + 21.7329 



+ 8.8899 



6 36 33.7778 



+ 

 + 



For 1795. 



7l. 171. 5. 



7 29 5.6310 



1 38 1.1459 



16 7.6124 



2 53.8634 



2 22.2377 



5 40 12.9738 



For 1755. 



h. m. s. 



7 29 5.6310 

 -2 27 1.7189 

 - 36 17.1279 

 + 9 46.7890 

 + 12 0.0783 



4 47 33.6515 



The corresponding values of a obtained from equations (6) are 



h. m. s. 



7 3 38.153 



h. fit. s. 



6 36 34.034 



k. m. 8. 



5 40 10.397 



h. 771. 8. 



4 45 55.203 



giving the deviations 



+ o!bi2 



+ 0^256 



2^577 



98.449 



