1113 



stellar cluster is jr =: 0",000159. ^) We can find now for eveij 

 apparent magnitude the corresponding absolute magnitude as 

 M = m—U.O. 



We can also calculate the mean colour-index for every absolute 

 magnitude, supposing the luminositj-curves in Messier 13 to be the 

 same as in our sjstem. These colour-indices have been put down 

 in the third column of the following table. The fourth column 

 contains the colour-indices observed by Shapley. 



The agreement between the third and fourth columns is sufficient. 



In this way Prof. Kapteyn has proved not only that we may not 

 conclude from Shapley's results that the distribution in stellar 

 clusters differs from that in our sidereal system, but also that his 

 observations give support to the hypothesis that in stellar clusteis 

 the same frequency of absolute magnitudes exists that we have 

 observed among the stars near the sun. 



By Hertzsprung a method has been indicated to determine the 

 parallax of stellar clusters containing ó Cephei variable stars, the 

 period of which is known. ') Miss Leavitt had shown in Periods 

 of 25 variable stars in the Small Magellanic Cloud, Harvard Circular 

 173, that there exists a linear relation between the logarithm of 

 their period and their brightness. 



The log. of the period increases by about 0.48 per magnitude. 



1) This parallax differs from the value .t = 0", 00040, which we found from the 

 catalogues of Ludendorff and Shapley, but it is, considering its accuracy, not at 

 variance with it. 



2) E. Hertzsprung, Ueber die raumliche Verleilung der Veranderlichen vom 

 5 Cephei Typus, A.N. 4692, Bd. 196, 201, 1913. 



