220 Prsesepe Group; Measurement and Reduction 



any one day from the readings of all the other stars that were 

 measured on that day. As we wish to have positive values of x 

 for those stars which have greater right ascensions than the central 

 star, we must subtract the reading " x direct" from the reading on 

 Star 15; but we must subtract the reading on Star 15 from the 

 reading " x reversed." Similiarly to get positive values of y 

 for those stars having greater declinations than the central star, 

 we subtract the reading on Star 15 from each " y direct " and the 

 contrary for "y reversed." 



4 Rotation Corrections. 



It was found very difficult to set the circle at exactly 90° plus 

 the reading for the previous day. Even when this had been ac- 

 complished the circle-reading was sometimes found to have 

 changed a little during the measurement of the stars. A correc- 

 tion is therefore necessary to reduce the rectangular coordinates 

 to what they would have been had the readings of the circle for 

 different days differed only by multiples of 90°. Let 



Q = the number of seconds which occurs most often in the cir- 

 cle readings of a particular plate. 



Q — i = the number of seconds in the reading for any day. 



Then we have,* 



Correction for x = — y. % sin 1." 

 " " y = + x. i sin 1." 



For the present measurements these corrections are very small, 

 never exceeding o/'os ; the}?- have however been applied through- 

 out. 



The values of Q adopted for the various plates are as follows : 



Plate I Q = 5" 



II o 



III o 



IV 58 



V 7 



VII o 



VIII 29 



IX 2 



5 Scale-value corrections. 



The scale being made of German silver has a greater coefficient 

 of expansion than the glass plate, and hence it would appear that 

 if the temperature changed during the measurement of a plate, 



* " Permanence of the Eutherfurd Photographic Plates " hy Harold Jacohy, 

 Annals of the N. Y. Acad, of Sciences, Vol. IX, p. 267. 



