24 



Sven Wicksell 



(51) ^a^-^'-*^ 1 -^ 



where a 2 and a, do not depend on Xj (at least when the limiting magnitude is < 6.0). 



Evidently the thing is of no consequence for our purpose as we determine 

 the constant q from the motions themselves, but it is of eminent importance when 

 we wish to find the constant \ { from the value found for q . Indeed, this is one 

 of the most actual desiderata of stellar astronomy. 



Clearly for all stars brighter than the magnitude m 



(52) 



j" a(m) dm = j* a{m) (m) dm. 



The consequences of this equation I have only studied numerically, assuming 

 that for the stars brighter than 6.0 we may put 



(53) a{m) = K, 3" 1 = K l e x ' m x = l.i 



Using this form for a(m) we must, however, fix a lower limit for the magni- 

 tudes. Unfortunately the result will depend considerably on the choice of this 

 limit. But as the stars brighter than 3.0 are only in number about Vio of the 

 stars brighter than 6.0 they will only slightly affect the value of 1%. Further the 

 number of stars brighter than 3.0 is too small for the formula (50) for the mean 

 parallax to be valid. Accordingly as a lower limit we fix the magnitude 3.0. Then 



dm. 



which gives 



or putting 



we have 



iyi* 



(x — sb XJ 

 x 



lb 



(1 — 0) s 1 — e 



\-sz (1 , 



The following small table will show the result for s = 2 





0.5 



0.6 



0.7 



08 



0.9 



1.0 



II., 



1.03 



1 04 



1.C6 



1 08 



1.11 





p 



1.03 



1.03 



1.03 



1.07 



1 10 





I 



