286 Prsesepe Group; Measurement and Reduction. 



sponds to a rotation of the axes, and is, therefore, of no impor- 

 tance when we determine the constants of a plate by comparing the 

 measured coordinates of some of the stars with their known places. 

 Turner's formulas are 



&X = kX-(i-\-H 2 ) -\-kYGH 

 AY=kX-GH + kY- (i -f- G 2 ) 



These formulas may be simplified when we use the above method 

 for determining the constants, as I pointed out in the Astronom- 

 ical Journal, No. 430 ; rejecting so much of the correction for re- 

 fraction as may be regarded as either an orientation correction 

 or a scale-value correction, we have remaining 



AX=kX-{H 2 — G 2 ) 

 AY= kX-2GH 



These formulas might have been used for the reduction of the 

 Prsesepe plates, but as we wished to know the true orientation and 

 scale-value for each plate, extra corrections to these constants 

 would have been necessary. Only four of the comparison stars 

 used need corrections for refraction; so that in the present case 

 nothing would have been gained by the use of the last formulas. 

 When, however, the number of comparison stars is greater, or 

 when we do not care especially to know the true orientation and 

 scale-value of a plate, these formulas will save some labor. 



