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C. V. L. Charlier 



approximately, in vertex and anti-vertex (T)^^ and C^) suggest the existence of two 

 star-streams, a suggestion that is not, however, confirmed by a mathemacal analysis. 

 True, I was thereby obliged to confine me — from reasons given above — to 

 the » abridged)) method sketched in Meddelanden Ser. B N:o 4, but — even if there 

 are some objections to be made against the apphcation of this method in the actual 

 case — the high values of the skewness (Sv') and the excess {Ev) in a direction 

 perpendicular to the direction to the vertex put it entirely out of question that the 

 observed values of the higher characteristics might be explained through the hypo- 

 thesis of two star-streams. 



33. We have, now, the choice between two possibilities: either the hypothesis 

 of the two-streams must be abandoned, or a value of the parameter must be 

 used, entirely different from that hitherto accepted by the astronomers. Whether 

 the latter alternative in reality might be reconciled with the two-stream hypothesis, 

 must, indeed, still be considered as an open question, but it is, certainly, a possi- 

 bility that must be taken into account. 



In any case, we must, according to my opinion, arrive at the conclusion that, 

 no positive evidence is as yet to hand for accepting the hypothesis of two star-streams 

 as an explanation of the observed proper motions of the stars. 



34. The characteristic features of the linear velocities of the stars, that are 

 to be » explained* are the ellipsoidal distribution of the velocities, the rather system- 

 atically distributed values of the skeivness, and the thoroughly negative values of 

 the excess. The ellipsoidal distribution together with the skew frequency curves 

 seem to suggest, most naturally, the existence of two or more star-streams. There 

 is an ingeneous modification — one might be inclined to say explanation — of the 

 two stars-stream hypothesis that has first been given by Turner at the meeting of 

 the R. A. S. March 1912. According to Turner we have to explain the observed 

 distribution of the proper motions »not from the meeting of two streams of parallel 

 motions, but from the convergence and divergence of stars visiting the gravitational 

 centre of our system». The hypothesis of Turner (which is as well applicable 

 to an elhpsoidal distribution of the velocities) has the advantage to open a possibility 

 to explain even the skew frequency distribution in a direction perpendicular to the 

 direction to the vertex. Such a skewness should, indeed, occur, if the position of 

 the sun were sufficiently near to — though, certainly, not coincident with — the 

 centre of our stellar system. For testing this hypothesis the most promising way 

 seems to be to determine the coordinates of the vertex, separately, from squares 

 situated at different parts of the heavens. Even the position of the apex should 

 be affected by such an hypothesis. I have tried to exanjine the hypothesis from 

 these points of view without being able, for the present, to give a conclusive answer 

 as to the efficiency of the hypothesis. 



35. In the kinetic theory of gases it is found that, in a mixture of several 

 gases, the mean energy of a particle is the same for all particles. In other words: 



