206 



SCIENCE 



[N. S. Vol. XXVI. No. 659 



past few months the results of researches 

 on stellar parallax, made under the direc- 

 tion of Dr. Elkin, at the Astronomical Ob- 

 servatory of Yale University, during the 

 past thirteen years,^^ have been published, 

 and they aiford a most crucial and entirely 

 independent check on the soundness of 

 Kapteyn's conclusions. 



COMPAEIS0I>r GEOUPS ARRANGED IN ORDER OF 

 PROPER MOTION 



GROUPS ARRANGED IN ORDER OF MAGNITUDE 



In considering the comparison between 

 the more or less theoretical results of 

 Kapteyn and the practical determinations 

 of Yale, we have to remember that Kap- 

 teyn's tables refer only to the means of 

 groups of a large number of stars having 

 on the average a specified magnitude and 

 proper motion, whilst the latter are direct 

 determinations affected by the accidental 



"■ Trans. Astron. Observatory of Tale Univ., Vol. 

 II., part 1. 



errors of the separate determinations and 

 by such uncertainty as attaches to the un- 

 known parallaxes of the comparison stars- 

 parallaxes which we have supplied from 

 Kapteyn's general tables. 



The Yale results consist of the deter- 

 mination of the parallax of 173 stars, of 

 which only ten had been previously known 

 to Kapteyn and had been utilized by him. 

 Dividing these results into gToups we get 

 the comparison given above. 



These results agree in a surprisingly 

 satisfactory way, having regard to the com- 

 paratively small number of stars in each 

 group and the great range of parallax 

 which we know to exist amongst individual 

 stars having the same magnitude and 

 proper motion. In the mean perhaps the 

 tabular parallaxes are in a minute degree 

 too large, but we have unquestionable proof 

 from this comparison that our knowledge 

 of stellar distances now rests on a solid 

 foundation. 



THE DISTRIBUTION OF VARIETIES OF LUMI- 

 NOSITY OF STARS 



But, besides the mean parallax of stars 

 of a particular magnitude and proper mo- 

 tion, it is essential that we should know 

 approximately what percentage of the stars 

 of such a group have twice, three times, 

 etc., the mean parallax of the group, and 

 what percentage only one half, one third of 

 that parallax, and so on. In principle, at 

 least, this frequency-law may be obtained 

 by means of the directly determined 

 parallaxes. For the stars of which we 

 have reliable determinations we can com- 

 pare these true parallaxes with the mean 

 parallax of stars having corresponding 

 magnitude and proper motion, and this 

 comparison will lead to a knowledge of the 

 frequency-law required. It is true that, 

 owing to the scarcity of material at present 

 available, the determination of the fre- 



