Group of the Pleiades. 259 



In reducing the Rutherfurd plates it will not be necessary to 

 pay any attention to the term 



— k tan z sin q tan 8 



already referred to above. For this term is a constant correction to 

 all the position angles of any given plate. It will therefore affect 

 the determination of the zero of position angles by the same amount 

 as it does the position angle of any star. Its effect upon the differ- 

 ence will therefore be nil. Finally, then, we may correct all the 

 distances and position angles by means of the following formulae : 



a — s = s x [tan 2 £ cos 2 (p — q) -\- i] X ( f\ 



7t — p = — x cosec i" tan 2 £ sin (p — q) cos ( p — q) ) 



but in the case of plates taken at considerable zenith distances, it 

 would be necessary to employ the more accurate formulae (c), and 

 the tables adapted to them. 



In practice it has been found convenient to prepare special tables 



of and 7t — p for each plate. The argument of these tables 



is p. The quantities were first computed for every io° of p — q 

 and then tabulated for every io° of p. They are strictly tables of 

 single entry, since £ and q are constants for the whole plate. The 

 refraction corrections were then taken from the tables by inspection, 

 the multiplication of the distance-refraction factor being effected 

 with Crelle's tables. The special refraction tables are given here 

 to facilitate any possible computations that may hereafter be under- 

 taken in connection with the Rutherfurd plates. 



It should perhaps be mentioned that a doubt exists as to whether 

 the Eastern or Western impression was made first, at the time of 

 observation. A careful consideration of all the existing evidence 

 on this point has led me to take the Eastern impression as the one 

 made first, and it is so marked in the table at the end of I. But it 

 is proper to say here that the final results would not be influenced, 

 if I had assumed the Western impressions as the earlier ones. The 

 effect of this assumption would be to interchange the letters W. and 

 E. in the table at the end of I., and the words West and East in 

 the headings of the tables now to be given. But since both impres- 

 sions have been made and measured, in the case of every star, and 

 on every plate, the mean of the results would not be affected by 

 interchanging the refraction corrections. 



