288 



THE SAYEE OBSERVATORY. 



(Pa 



For -gjf the Eight Ascension and Declination were reduced to 1825 and 1925, using 



for this purpose the first and second differential coefficients already computed. % was 



then derived for these dates, the differences giving -^ with all necessary precision. 

 For checking these values the tables given by Gould* were employed from 0" to 12", 

 neglecting proper motion. From 12 h to 24" the tables of Oppokerf were similarly 

 used. 



As already stated the catalogue places were reduced to Auwers' system whenever 

 the necessary corrections were available. A correction for proper motion was also 

 applied in all cases where the necessary data could be found. 

 Let t be the epoch of the catalogue, 



t the mean date of observation, usually different from t, 

 fj." the proper motion employed in forming the catalogue, 

 ft the proper motion assumed in this discussion, 

 The correction will be (t — /) (ji — ft") = ^a. 



It is perhaps superfluous to state that both / and [i" are unknown in case of many 

 of the older catalogues. 



Let n be the difference between the corrected catalogue place and the assumed place, 

 reduced as above explained to the epoch of the catalogue, 

 Then each catalogue furnishes an equation of the form 



l/p (An: -|- TAfi = mn) 



In which p is the weight of the catalogue place, 



Aa the correction to the assumed Declination, or Eight Ascension, 

 A;x the correction to the assumed proper motion, 

 T=1875 — t. 

 A least square solution gives the most probable values of Aa and Aft. 



The method of solving the equations is one very commonly employed in cases like 

 this and is as follows : 



Let t be the weighted mean of the catalogue epochs, or of the epoch of observa- 

 tion when this differs from that of the catalogue, 



t\, t'2. L the epochs of the respective catalogues, 



r A, T 2 T n = (l x - t Q ), ( k _ to ) (t n _ to ) 

 XpT should be zero. 



* Oatdlogo de Las Zonas Entelares, Appendix, Tabic iv, Cordoba, 1884. In using this tabic it must be 

 remembered that the value of p» as given in column four should be doubled. See Ast. Nach., Bd. 137, p. 295. 

 f Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. i, Table XII. 



