464 POPULAR SCIENCE MONTHLY. 



stars per 100 square degrees having a proper motion of 10" or more. 

 This ratio would give about 10,000 for the whole heavens. The sphere 

 corresponding to this limit of proper mo don is 60R. On our hypothesis 

 as to star density this sphere would contain 27,000 stars, nearly three 

 times the number derived from Auwers's work. But it is not at all 

 unlikely that even this sphere in question contains twice as many 

 stars as have been detected. Great numbers of the more distant stars 

 will not have been catalogued, owing to their faintness, because a 

 star at the distance 60R will shine to us with only one per cent, the light 

 of one at distance 6R. This corresponds to a diminution of five 

 magnitudes; that is to say, a star of the sixth magnitude at distance 

 6E would only be of the eleventh magnitude at distance 60E, and 

 would, therefore, not be catalogued at all. There is, therefore, no 

 reason for changing our estimate of star density, which assigns to each 

 star around us 8 units of volume in space. 



This fact suggests another important one. Owing to the great 

 diversity in the absolute magnitude of the stars, those we can observe 

 with our telescopes will naturally be more crowded in the neighborhood 

 of our system than they will at greater distances. 



Some further results as to the mean parallax of the stars may be 

 derived from a continuation of the statistical study of the proper 

 motions. Kapteyn's investigation in this direction includes a de- 

 termination of the mean parallactic motion of the stars of each magni- 

 tude for the first and second spectral types separately. From this he 

 obtains the following mean parallaxes for stars of the different mag- 

 nitudes: 



Mean parallaxes of stars of different magnitudes, and of the two prin- 

 cipal types, as found from their parallactic motions: 

 Mag. Type I. Type II. 



2.0 .0315 .0715 



3.0 .0223 .0515 



4.0 .0157 .0357 



5.0 .0111 .0253 



6.0 .0079 .0179 



7.0 .0056 .0126 



8.0 .0039 .0089 



9.0 .0028 .0063 



10.0 .0020 .0045 



11.0 .0014 .0032 



Using the value 4 for the solar motion, instead of 3.5, found by Kapteyn, 



all these parallaxes should be diminished by one-eighth of their amount. 



Unfortunately, owing to the great diversity in the absolute bright- 

 ness of the stars, and the resulting great difference in the distances 

 of stars having the same magnitude, these numbers can give us only 



