Summary. 
1) The essential feature of the present investigation is that it is 
based on the individual brightness of the stars. Moreover their proper 
motions and radial velocities are taken into consideration as far as these 
characteristics are known. 
2) In the statistical investigations hitherto made the proper motion 
of a star of, say, the 6" magnitude is directly compared with the proper 
motions of a star of the first magnitude, though the latter corresponds 
to a linear motion ten times as great as the linear motion of the former 
star, if both stars are supposed to possess the same luminosity and 
apparent motion, 
3) One consequence of this treatment is that the resulting mean 
values of the distances and motions of the stars are subject to great 
mean errors and, what is more serious, sometimes even to consider- 
able systematie errors. 
Let us consider for a moment a group of stars, all having the 
same (absolute) luminosity. The distance (r) of each individual star is 
determined by the apparent magnitude, m, and a single parameter, 
which we will call 2. We have 
Y= R 109: m. 
The parameter À is equal to the distance of a star of the appa- 
rent magnitude 0... We may express the same thing by saying that a 
star of the apparent magnitude m, when placed at a distance equal 
to À, will have an apparent magnitude equal to 0.o. 
The value of R is evidently not the same for all stars. It varies, 
however, much less than 7. It is found, indeed, that, with a few excep- 
tions, À has, for all stars, a value smaller than 10 Siriometers, whereas 
r may amount to 300 Sir. or more. It would hence be appropriate to 
introduce À as a parameter instead of r, even if no regard were paid 
to the different luminosities of the stars. 
