502 BURNS— RELATIVE AND ABSOLUTE PARALLAXES. 



tion, as given by Kapteyn, and the assumed parallax, o". 003-5. 

 There is no reason to suppose that the mean velocity of the faint 

 stars is any greater than that of the brighter ones, although one 

 might get that impression from an examination of the velocities 

 which have been determined to date. This arises from the fact 

 that the faint stars which have been observed for radial velocities 

 have been chosen largely because of their large proper motion and 

 they are mainly objects of great total velocity. Our direct knowl- 

 edge of the velocity of the average faint star is practically nil. 



The mean distance of the faint stars can be inferred from 

 statistical discussions of the brighter stars, as has just been done, 

 or computed more surely by means of radial velocities after rep- 

 resentative objects have been observed. Yet there is no means of 

 being sure of the exact parallax of the stars as faint as the ninth 

 magnitude without actually comparing a considerable number of 

 them with stars a good deal fainter, by trigonometric methods. 

 The complete observation of all the so-called interesting objects 

 jon our programs will leave us about where we are now as far as 

 Ihe average faint star is concerned. On the other hand, an observ- 

 a.tory devoting its parallax sessions to the subject could in a few 

 3^ears find the parallaxes of those objects of unusual interest, the 

 xepresentative star of each of the magnitude groups 6.5 to 9.5 ; that 

 is, their parallax relative to stars of the 13th magnitude. 



Conclusions. 



A simple method of computing mean parallaxes from observed 

 radial velocities and total proper motions is outlined, and results 

 derived by this method are compared with those obtained by means 

 of the tau component. 



Observed and computed parallaxes of stars brighter than 5.1 

 visual are compared in order to find the mean parallax of the com- 

 parison stars. This value is seen to be o".oio. Other considera- 

 tions leading to a value of o".oo7 to o".oo9 are discussed. 



