Studies in Stellar Statistics 



41 



(Meddel. N:o 34). These objections are however irrelevant or at least weakened it 

 the statistical material is properly treated. 



First it may be remarked, tbat the frequency curves for the proper motions 

 are of type B) (compare the § 22) and that accidentally large values of 

 p will greatly influence the resulting mean value of p. This is a serious 

 inconvenience, that however can be, in a large part, avoided through the treatment 

 that will be explained in she following. Secondly it must be observed that the constant 

 in (69) is not the same all over the heaven. This constant, indeed, according 

 to the 13th § depends on the mean value — M{P) — of the projected linear 

 velocity and this mean value differs, because of the motion of the sun and of the 

 systematic motions of the stars, from one square to the other. It is hence necessary 

 to determine X from each square separately and then to use the available values 

 of the parallaxes to determine from (69*). Though the values of M{p) from 

 observations all over the heaven are of no direct use for our purpose, we may 

 however through such observations get an indication of the solution of the problem. 



I give in the following table the value of the mean proper motions for different 

 magnitudes for the BsADLET-stars. The values of the proper motions are taken 

 from Kapteyn's memoir in the Publications of the Laboratory of Groningen N:o 9. 



Tab. 9. Bradley stars. Correlation between mean 

 motion and magnitude. 



m 



M ip) 









n 



— V" to 4- 2'".0 



0".428 



20 



0".000 to 0".050 



5"'.51 



1356 



2 .0 » 3 .0 



0 .120 



53 



0 .050 » 0 .100 



5 .54 



621 



3 .01 » 3 .50 



0 .130 



77 



0 .100 » 0 .150 



5 .31 



246 



3 .51 » 4 .00 



0 .186 



105 



0 .]50 » 0 .200 



5 .01 



125 



4 .01 » 4 .50 



0 .142 



185 



0 .200 » 0 .250 



4 .77 



79 



4 .51 » .5 .00 



0 .105 



329 



0 .250 » 0 .500 



4 .99 



129 



5 .01 » 5 .50 



0 .092 



504 



0 .500 3 0 .700 



4 .65 



34 



5 .51 > 6 .00 



0 .079 



580 



0 .700 Î 1 .000 



4 .60 



10 



6 .01 > 6 .50 



0 .088 



421 



> 1".000 



4 .07 



16 



In the 5th column are given the mean magnitudes corresponding to different 

 classes of mean motions. — The above numbers cannot be used for calculating 

 X (and K^) if for no other reason because the fainter stars (from 5th) are only 

 very incompletely represented. 



21. It might be proposed to determine n as function of m directly from the 

 observed parallaxes. For the present this must however be considered as inpracticable 

 and it may be doubted it such a determination even shall succeed. It might however 

 be possible to use the parallaxes for determining the frequency curve for the ab- 

 solute magnitude. I shall preliminaryly examine the result of such an investigation. 



First we shah fix our units of distance and magnitude. As unit of distance 

 I shall choose a distance equal to a million times the mean distance of the sun 



Lunds Univ:s Årsskrift. N. P. Afd. 2. Bd 8. 6 



