24 



C. V. L. Charlier 



13. For deduciDg the (relative) distance of a cluster from the apparent 

 magnitude of the stars in the cluster we ought to know tlie mean apparent magni- 

 tude of all stars in the cluster. This may perhaps he deduced for ordinary clusters, 

 but is very difficult to determine for the globulars (compare in this respect the 

 research of Zeipel on M. 3 in Arkiv f. Mat., Astr. och Fysik, Bd 11, 1916). To 

 start from the magnitude of the brightest stars in each cluster would give rise to 

 some additional uncertainty (besides that arising from the assumption that all 

 clusters would be composed of stars within the same limits of absolute magnitude). 

 That however an appreciable correlation exists between the brightest magnitude of 

 the stars and the distance may be concluded from the following correlation table. 



Correlation between the diameter of a globular cluster and the magnitude 



of its brightest stars. 



Apiiarent magnitude 





10 



11 



12 



13 



U 



15 



16 



Faint 



Sum 



Mean 

 nnairn 



2' 







1 



2 



6 



5 



8 



4 



21 



14 4 



5 







1 



2 



5 



1 







9 



13.7 



8 







3 



6 



1 







1 



11 



12.8 



11 







1 



3 



1 









5 



130 



14 







2 



1 





1 







4 



13.0 



17 





1 















1 



11.0 



20 









i 











1 



13.0 



23 



1 

















1 



10.0 



26 























29 









1 











1 



13.0 



32 























35 









1 











1 



13.0 



Sum 



1 



1 



8 



17 



13 



7 



3 



5 



55 





Mean 

 diniii. 



23 



17 



8.8 



11.4 



4.3 



4.1 



2.0 



33 







There are 55 globular cluster for which Bailey has given the apparent magni- 

 tude of the stars as well as the diameter of the cluster. In 5 cases the brightest 

 magnitude has been given as »faint», i. e. fainter than the 16:th magnitude. 



The last line gives the mean diameter of the 'cluster in each column. The 

 last column gives the mean magnitude of the clusters in each line. The mean 

 magnitudes come out rather uncertain, no less than 5 diameter groups having only 

 one representative. The mean diameters corresponding to different magnitudes are 

 better determined. The coefficient of correlation amounts to — 0.49, a smaller value 

 than could have been a priori expected. 



