274 Rutherfurd Photographic Measures. 



Pv Pi> P\" > ■ ■ ■ Pi n — the position angle of the first star on the 



various plates. 

 p 2 , p 2 , p 2 fr , . . . p 2 n = the same for the next star, and so on. 



And put : 



*. = £(JP*4-P,' +..-. +P, n ) 



Then P v P 2 , . . . . are the mean values of position angles which we 

 obtain if we apply no systematic corrections. The correction for 

 the first plate will be : 



(Pi - A) + (ft - P 2 ) + • . . + (Ps- P.) 



s 

 and for the second plate : 



(p/ - A) + (p: - p 2 ) + . . . + (p/ - ^) 



s 

 and so on for the other plates. Now if we introduce into these last 

 expressions the values given above for P v P 2 , . . . P s , we find that 

 the sum of all the corrections is zero. It is therefore obvious that 

 if we were to apply the corrections, we would get for the mean 

 values of the position angles, P v P 2 , . . . . P 8 as before. Thus the 

 final values are not changed by the proposed process.* But the 

 inter-agreement of the separate values of any position angle might 

 be very much improved by applying the corrections. This arises 

 from the fact that the uncorrected position angles involve the error 

 made in observing the star, as well as that belonging to the zero 

 point, while a portion of the latter error would be practically re- 

 moved by applying the corrections. If we compute the probable 

 errors in the usual way, we shall get larger values than would 

 result if the corrections were introduced. Investigation shows, 

 however, that their introduction would diminish the probable errors 

 by less than one-fifth ; so that we are justified in omitting them 

 altogether. 



* The sum of the corrections applied by Gould in his reduction (already 

 referred to) of the Prsesepe plates is exactly zero. In the case of the Pleiades 

 plates, the sum is — 10" for the Eastern impressions, but for the Western it 

 is — i' 31". This last may be due to a typographical error. 



