220 Proceedings of the Royal Irish Academy. 



By the application of these several corrections, the observed dis- 

 tance and position angle of the two stars is transformed into the true 

 distance and position angle when the stars are situated in their mean 

 positions on 1st January, 1875. 



The following catalogue contains the results of these observations 

 for forty-two different objects selected from the working list, of 

 which the construction has been already explained. The first column 

 of the catalogue contains the number of the object for convenience 

 of reference. The second column gives the designation of the object. 

 Prequent reference is here made to the list of Eed Stars compiled by 

 Schjellerup (Yierteljahrschrift der Astronomischen Gesellschaft ix. 

 Jahrgang). This catalogue is referred to by the abbreviation " Schj." 

 (Red). In other cases (as, for example, No. vi.) the reference 

 (+ 27°, 1270) is, as usual, to the " Durchmusterung," vols, iii., iv., v., 

 of the JBonn Observations . No. xxxi. is a Hed Star from Mr. Bir- 

 mingham's Catalogue {Transactions of the Boyal Irish Academy, voL 

 xxvi., pp. 249-354). 



The third column gives the date of the observation, which 

 is always as near as possible to one of the two critical dates 

 already referred to. In connexion with these critical dates, it 

 is to be remembered that they have been chosen without reference 

 to the comparison star, and therefore are not generally the pre- 

 cise dates at which parallax would make the maximum derange- 

 ment of either the distance or the position angle. They are only 

 the dates at which the star is situated at the apses of the paral- 

 lactic ellipse. If the comparison star happened to be situated in the 

 direction of the minor axis of the parallactic ellipse, there would be 

 no parallactic change in the distance at the two dates, but there 

 would be the greatest change possible in the position. On the other 

 hand, if the comparison star were situated on the major axis of the 

 parallactic ellipse, there would be the greatest change possible in the 

 distance. It might, no doubt, have been better, in some respects, to 

 have chosen the dates so that absolutely the maximum alterations of 

 distance and position should have been secured, but this would have 

 involved more time than I cared to devote to work which might pro- 

 bably lead only to a negative result. This method would, generally, 

 have required five observations. The first of these would be devoted 

 to the selection of a suitable comparison star, and a determination of 

 its place ; then, from these results the four dates of maximum and 

 minimum derangement of distance and position, respectively, would 

 have been determined, and the observations would have to be renewed 

 at or near these dates. I have, therefore, adopted the simpler method,, 

 which only requires two observations, these being generally about the 

 dates when the star is at its greatest distance on one side or the 

 other of its mean place. 



The fourth column gives the corrected distances, and the fifth 

 column contains the corrected values of the position angles. 



