252 DETERMINATION OF THE LONGITUDE OF SEVERAL 



X = [5-3645163] . (/ — e*" 0°^ 0^) 



X' = [0-42800] t . (t —.12' O'" 0^) 



X" = [9.5229] XX' 



X'' = [9.6499] X' . (/ + 12'' 0-" 0') (/ — 24' 0" 0^) 



*X'" = [9.3010] XX". 



SECTION VI. 



The observed increase of the right ascension of the moon's bright 

 limb, as derived directly from the lists of moon-culminations, requires 

 a correction, when the same stars have not been observed at both places, 

 as vv^ell as when the number of wires used at each place is not uniform. 

 The formula for computing this correction has been derived from a 

 combination of Gauss's application of the calculus of probabilities to 

 the reduction of moon-culminations, as given by Nicolai, Astr. Nachr., 

 No. 26, with Dumouchel's method, No. 125 of the same, for the dif- 

 ferent stars. Thus, for the European observatory and western station 

 respectively, let 



the observed R. A. of a star, 

 A' — A for the same star, 

 a similar value for another star, 

 the number of wires on which each limb was ob- 

 served, 

 similar values for a star, 



ir 



A' 



and A 







E 







E 



/ 



and 



/' 



a 



and 



a' 



^ = J , J/ , for the moon's limb. 



a = — ; — - , for one star, 

 a-\-a 



fi' = B. similar value for another star, 



£ = the correction of the observed increase of the right 



ascension of the moon's bright limb, 



S = symbol to denote the aggregate of similar quantities. 



Then we have, 



* This term is not required for reducing moon-culminations. 



