( 137 ) 



XIII that form the transition from F to G ; for the hiter stages of 

 development the brightness again increases. 



§ 3. A better measure than the proper motion for the mean 

 distance of a group of stars is the parallactic motion. This investiga- 

 tion was rendered easy by means of W- 9 of the "Publications of 

 the astronomical Laboratory at Groningen", where the components 

 T and V of the proper motion are computed with the further auxiliary 

 quantities for all the Bradley-stars. Let t and v be the components of 

 the proper motion at right angles with and in the direction of the 

 antapex, X the spherical distance of the star-apex, then 



2 V sin X 



2 sm* X 

 is the parallactic motion for a group of stars, i.e. the velocity of the 

 solar system divided by the mean distance of the group. The mean 



1 

 of the other component — ^ t is, at a random distribution of the 



71 



directions, equal to half the mean linear velocitj^ divided by the 

 distance. 



The mean magnitudes of the different groups are also different. 

 Because we here especially wish to derive conclusions about the 

 brightness, and as both the magnitude and the proper motion depend 

 on the distance the computation was made after the reduction to 



^) The Roman figures in italics in Maury's classification designate the transition 

 to one class higher. 



