STRUCTUEE OF THE UNIVEESE KAPTEYN, 



315 



In other words, the sun's absohite magnitude is 10.5. A star of 

 absohite magnitude 9.5 will, therefore, have 2.5 times the light- 

 power — that is, 2.5 times the luminosity of the sun. A star of abso- 

 lute magnitude 8.5 will again have a luminosity which is 2.5 times 

 greater, and so on. 



Such results evidently enable us to transform our absolute magni- 

 tudes into luminosities. Thus translated, I found the results shown 

 in the following table. 



LUMINOSITY TABLE. 



Within a sphere having a radius of 555 light years, there must 

 exist : 



This table represents what, up to the present time, we know about 

 the mixture law. 



The fainter the stars, the more numerous. 



The rate at which the numbers increase with the faintness is par- 

 ticularly noticeable for the very bright stars. 



Passing to the fainter stars, this rate gradually diminishes, and it 

 looks as if we must expect no further increase in number for stars 

 whose luminosity falls below one-hundredth of that of the sun. 

 Meanwhile this is simply a surmise. For stars of this order of faint- 

 ness data begin to fail. Here, as in nearly every investigation about 

 the structure of the stellar system, the want of data for stars below 

 the ninth apparent magnitude makes itself very painfully felt. 



But let us come back to our figure 4. I will first remark that, 

 knowing the mixture law, we can predict the number of stars that we 

 shall get in the empty boxes belonging to the ninth, tenth, etc., magni- 

 tude, as soon as continued astronomical observations will permit us 

 to include these stars in our discussion. For the mixture law, as 

 derived just now, shows that in our universe the stars of absolute 

 magnitude 4.5 is 5,400 (fig. 4), there must be 3.5 times 5,400, that is, 

 magnitude 4.5. 



Now as in the eleventh shell the number of stars of the absolute 

 magnitude 4.5 is 5,400 (fig. 4), there must be 3.5 times 5,400, that is, 

 18,900 stars of absolute magnitude 5.5 in this shell. These belong all 

 in the box of the ninth apparent magnitude of this shell. In the 



