104 



C. V. L. Charlier 



We have found in I that this constant differs but little from 3.0. As to , its 

 value is, however, very imperfectly iinown. It may be derived either from the 

 systematic parallaxes of the stars of different magnitudes, or from the dispersion 

 (og) of the absolute magnitudes of the stars. The former method seems, for the 

 present, to be somewhat surer, but is, nevertheless, very untrustworthy. From a 

 discussion of the proper motions of the stars of the 4:th and the 5:th magnitude, 

 I arrive, in this memoir, at a value X-^ = 0.20, whereas an investigation of Kapteyn, 

 of a larger material, leads to the value = 0.65 ^). 



Fortunately an error in X^ has but little influence on the value of q, at least 

 if X^ does not be very near to zero or to unity. If X^ has a value enclosed between 

 the limits 0.26 < X^^ < 0.76 — what is on different grounds probable — the value 

 of q differs only little from n = L.27, a value used in the investigations of this 

 memoir. The question must, however, for the present be left open, whether a value 

 of outside these limits might be compatible with the systematic parallaxes of the 

 stars, as well as with the dispersion of their absolute magnitudes. 



Starting from this value of g, I first deduce, from the proper motions in 

 Boss' catalogue of the stars brigliter than the sixth magnitude, the characteristics 

 of the linear velocities of the stars for each one of the 48 squares, into which the 

 sky here has been divided (compare plate VI). 



The characteristics (moments) of the first order lead to the determination of 

 the apex. Treating, separately, the stars of the 4:th and 5:th magnitude, I obtain 

 for the right ascension (A) und the declination (D) of the apex the following values: 



From stars of the 4:th magnitude: 



A = 267".18 ± 3«.59, 

 D = + 340.59 ± 2» 96. 



From stars of the 5:th magnitude: 



A-- '273«.i7 ± 2".0H, 



D= +31°.1B± P.76. 



Putting, with Campbell, the velocity of the sun equal to 20 km per second, 

 I furthermore obtain for the mean parallax M{'k) of the stars of the fifth magnitude 

 [m = 5.6) the value 



üf^ Jti) = 0".01t26 ± 0".00042, 



whereas the mean distance of the same stars was found to be 



Jf^ (r) = 29.53 ± l.ii Siriometers. 



When deriving the mean value of the parallax from the mean value of the 

 distance (or vice versa) it is necessary to observe that the mean value of - is not 

 the inverse of the mean value of r, but we have 



^) From the research of Comstock: Astr. Journal N:r 558 (1904) I derive the vakie X^ = 0.56. 



