August 16, 1907] 



SCIENCE 



207 



quency-law is not so strong as may be de- 

 sirable, but further improvement is simply 

 a question of time and the augmentation 

 of parallax-determination. 



Adopting provisionally the frequency- 

 lavif found in this way by Kapteyn,-- we 

 can localize all the stars in space down to 

 about the ninth magnitude. 



Take, for example, the stars of magni- 

 tude 5.5 to 6.5. There are about 4,800 of 

 these stars in the whole sky. According to 

 Auwers-Bradley, about 9^- per cent, of these 

 stars, or some 460 in all, have proper mo- 

 tions between 0".04 and 0".05. Now, ac- 

 cording to Kapteyn's empiric formula, 

 whose satisfactory agreement with the 

 Tale results has just been shown, the 

 mean parallax of such stars is almost 

 exactly 0".01. Further, according to his 

 frequency-law, 29 per cent, of the stars 



tude in the same way, we finally locate all 

 these stars in space. -^ 



It is true we have not localized the indi- 

 vidual stars, but we know approximately 

 and Avithin certain limits of magnitude the 

 number of stars at each distance from the 

 sun. 



Thus the apparent brightness and the 

 distance being known we have the means 

 of determining the light-energy or abso- 

 lute luminosity of the stars, provided it 

 can he assumed that light does not suffer 

 any extinction in its passage through inter- 

 stellar space. 



On this assumption Kapteyn was led to 

 the following results, viz., that within a 

 sphere the radius of which is 560 light- 

 years (a distance which corresponds with 

 that of the average star of the ninth magni- 

 tude) there will be found: 



have parallaxes between the mean value 

 and double the mean value; 6 per cent, 

 have parallaxes between twice and three 

 times the mean value ; 1^ per cent, between 

 three and four times the mean value. 

 Therefore of our 460 stars 133 will have 

 parallaxes between 0".01 and 0".02, 

 twenty-eight between 0".02 and 0".03, 

 seven between 0".03 and 0".04, and so on. 

 Localizing in the same way the stars of 

 the sixth magnitude having other proper 

 motions, and then treating the stars of the 

 first magnitude, second magnitude, third 

 magnitude, and so on to the ninth magni- 



'^ Publications Astron. Lab. Groningen, No. 8, 

 p. 23. 



^Z6id., No. IL Table II. 



THE DENSITY OF STELLAR DISTRIBUTION AT 

 DIFFERENT DISTANCES FROM OUR SUN 



Consider, lastly, the distribution of 

 stellar density, that is, the number of stars 

 contained in the unit of volume. 



We can not determine absolute star- 

 density, because, for example, some of the 

 stars which we know from their measured 

 parallaxes to be comparatively near to us 

 are in themselves so little luminous that if 

 removed to even a few light-years greater 

 distance they would appear fainter than 

 the ninth magnitude, and so fall below the 

 magnitude at which our data at present 

 stop. 



~But if we assume that intrinsically faint 

 and bright stars are distributed in the 



