stellar olnsters 



25 



The correlation between the diameter of a cluster and the number of stars 

 in the cluster as counted on the Harvard photographs is shown from the following 

 table. 



Correlation between the number of stars and the diameter 

 of a globular cluster. 



Number of stars 





Few 



100 



250 



400 



550 



700 



850 



1000 



2000 



8000 



5000 



6000 



Sum 



Mean 

 muj^n . 



2' 



2 



13 



2 



3 







1 



1 











22 



240 



Ô 



- 



2 



3 



1 



1 



— 





2 



— 



— 



— 



— 



9 



430 



8 



— 



1 



2 



4 







1 



3 





— 







— 



11 



550 



11 







1 







1 





2 



1 









5 



1000 



li 







1 











1 



1 





1 







4 



1300 



17 











1 

















1 



550 



20 

















1 











1 



1000 



23 







1 





















1 



250 



26 































29 























1 





1 



5000 



32 































35 

























1 



1 



6000 



Sum 



2 



16 



10 



8 



2 



1 



8 



10 



1 



1 



1 



1 



56 





Mean 

 diam. 



2 



2.8 



8.3 



5.4 



11.0 



11.0 



8.0 



9.2 



11 



14 



29 



35 







The coefficient of correlation amounts to -f- ().7ß and hence greater than in 

 the former case. 



14. The integrated magnitudes of the globular clusters are generally not 

 known, bat there is no serious obstacles for determining them through observations. 

 They would furnish us with valuable contributions to our knowledge of the relative 

 distances of the clusters and moreover put us in the position to get an appreciation 

 of the number of stars contained in the clusters. 



Consider an assembly of stars all having the same apparent magnitude, ?», 

 and let \). be the integrated apparent magnitude of the assembly. If h is the appa- 

 rent brightness of a si)igle star, the apparent brightness of the whole assembly is 

 7ih, 11 being the total number of stars. We hence have 



Eliminating h wc get 

 (16) [J. = yn — 2.5 log n , 



which is the formula connecting the apparent magnitude of a single star and that 



4 



