1111 



the number of stars of a fixed absolute magnitude, we shall tind the 

 foregoing table. 



In this table ' have also been mentioned the mean colour-indices, 

 which we iind for every absolute magnitude, if we employ for every 

 type colour-indices used by Shapley. Although the way in which 

 the spectra ai'e divided varies greatly, yet the average colour for the 

 various absolute magnitudes is nearly the same. From this we may 

 conclude, what might also ha\e been understood beforehand, that it 

 is difficult to form an opinion about the division of the spectra from 

 the mean colour-indices. 



Shapley's results have been compared, whenever this was possible, 

 with the above table. In large outlines they were found to correspond. 

 To compare them minutely would, however, serve no purpose, because: 



1^"^ Schwarzschild's results have only a preliminary value; 



2"^ Shapley did not, in various instances, determine the colour-indices 

 for- all stars of a certain magnitude and we have no certainty that 

 the stars he made use of, are lepresentative; 



3ixi ^ve cannot decide which stars do or do not belong to the 

 cluster ; 



4^^! Shapley's hypothetical colour-classes are not identical with 

 the usual spectral types or need not be so ; 



5^'' our determinations of parallaxes always leave some doubt 

 as to the absolute magnitudes which may even be a cou[)le of 

 magnitudes larger or smaller. 



We cannot by this method ascertain with absolute certainty whether 

 from Shapley's observations must be concluded that the distribution 

 of colours in stellar clusters differs from the one in our system of 

 stars. By Prof. Kapteyn this problem has, however, been solved in 

 another way in an article not yet published. He was so kind as to 

 communicate to me on this subject what follows: 



Shapley found that the absolutely bright stars in Messier 13 are 

 redder than those that are less bright. Now it is a well-known fact 

 that in our system the white stars are on an average absolutely 

 brighter than the red ones. At first sight these facts seem to contradict 

 each other. But the seeming contradiction disappears if we take into 

 consideration what follows : 



Limiting ourselves to a comparison of the luminosity-curves of K 

 and B stars, we find that the mean absolute brightness of the K 

 stars is indeed much inferior to that of the B stars, or in other 

 words, that the luminosity-curve of the /iT stars spreads itself around 

 an absolute brightness, which is much inferior to that of the B 



