STKUCTUEB OF THE UNIVEKSE KAPTEYN. 



313 



Further than for the eleventh shell no numbers have been entered. 

 They become too uncertain. As, however, we know the total number 

 of stars of each apparent magnitude, Ave know the aggregate number 

 Avhich remains to be distributed over the whole of the farther shells. 



What has here been explained for the stars of the fifth magnitude, 

 has been also done for the other magnitudes between the second and 

 the eighth. The whole of the results are shown in our figure 4. 



\^m^ -years 



Fig. 4. — Distance Boxes, reconstructed diagram. 



STARS OF EQUAL LUMINOSrrr BROUGHT TOGETHER. 



The main result of the investigation is embodied in these numbers — 

 and first, in every box stars have now been brought together of equal 

 absolute magnitude — that is, of equal luminosity. For as the stars 

 in each box are at the same distance, and as, at the same time, they 

 are of equal apparent brightness, they must, of necessity, be of equal 

 total light-power; that is, according to our definition, of equal lumin- 

 osity, or absolute magnitude. For the absolute magnitude of a star, 

 I have taken the magnitude the star would show if placed at a dis- 



