Introduction. 



Ever since the day when it was announced that the peculiar motions of the 

 stars are not distributed in a Imp-hazard way to give preference to no certain di- 

 rection, a distribution that had before been regarded as nearly an axiom, many 

 astronomers have been working at the problems involved in defining the nature of 

 this distribution and its bearings on our knownledge of the stellar universe. It has 

 then been mainly two different hypotheses that have gouverned the ideas; the 

 hypothesis of two star-streams proposed by Kapteyn and the ellipsoidal hypothesis 

 of Schwartzschild. As long as it was only a matter of choosing a function of 

 interpolation the two-stream hypothesis answered its purpose best as it involves 

 one more parameter than the rival hypothesis. But when it comes to the bearings 

 on the nature of the stellar system, the ellipsoidal hypothesis is to be preferred, it 

 being by far the most simple of the two, and more fertile for generalisation. Besides 

 the two-stream hypothesis supposes a dual character of the Milky Way, an assump- 

 tion which it is repugnant to make without necessity. 



When we take the material for the investigation from the proper motions, the 

 question of the distribution in space of the stars is met with. Clearly here is .the 

 ground for more assumptions and hypotheses. To escape this question most authors 

 on the subject have refrained from regarding the magnitudes of the motion contenting 

 themselves with making a statistics of the position angles. However, one circum- 

 stance has hereby not been duly accentuated. That is, that the characteristics of the 

 distribution obtained from the statistics of position angles do not necessarily refer 

 to the linear motions of the stars. Really they are as much a property of the 

 apparent motion or any other system of stellar motion and positions in space feasible 

 to produce the observed proper motions. The only knowledge obtained is that if 

 the assumptions regarding the qualities of distribution of the linear motions are 

 true, then the parameters have the values found. Nothing in the nature of proving 

 the truth of the assumptions is furnished. 



In order to give a description as good as possible of the distribution of the 

 linear peculiar motions of the stars we must regard also the amounts of the motions. 



