Permanence of the Eutherfurd Photographic Plates. 267 



measures were made. Since it is immaterial what the absolute 

 length of our linear unit may be, we shall assume that the cor- 

 rected values so obtained for x^ — xj and y^ — y/ in these special 

 standard measures are the true values of these quantities. Here- 

 after, in speaking of x^ — xj and y^ — yj^ we shall always mean 

 the corrected values of these quantities obtained from those di- 

 rectly measured in the manner just explained. 



For any other set of measures, in which we find the values to be : 



x—x', y—y', 



the corresponding position circle error being i, we must calculate 



the corrections as follows. 



To correct for the angle error, we must add to every measured 



X, the quantity : 



— ii/sin i" 



and to every measured y, the quantity : 



-\-ixsva.i." 



To correct for the scale errors, we must add to every measured 

 X the quantity : 



/ X — x' \ 



and to every measured y, the quantity : 



yU- y-y' \ 



*V ys — ys'J 



It is to be noted that in using these formulae the proper signs 

 must be affixed to the measured values of the coordinates. These 

 measured values are obtained by simply subtracting the scale- 

 reading obtained for the central star from the scale-reading ob- 

 tained in the measure of any other star. The signs given to the 

 X and y obtained in this way depend on the following rule : 



The ^-coordinate of a star is positive if the right ascension of 

 the star is greater than that of the central star. The ^/-coordi- 

 nate of a star is positive if the star is nearer than the central star 

 to the North pole of the heavens. 



The following Table gives the values of the quantity : 



i sin i" X lo* 

 for each of the plates measured. Plate i6 appears twice in the 



