Stellar dusters 33 



Denoting the absolute magnitudes corresponding to these three units of distance 

 by M, il/j and ^ respectively, we have the following relations 



iü^^^ = Tlf + 1.B7, 



as directly follows from the relation 



m = M -\- 5 log r, 



= M — 5 log TT — 3.428, 



between apparent and absolute magnitudes. 



The absolute magnitudes used in this memoir refer to a siriometer as unit of 

 distance and shall be denoted by M. 



Which are the absolute magnitudes of the stars belonging to a globular cluster? 



In table 2 are given, according to Bailey, the apparent magnitudes of the 

 stars in the clusters on the photographs at Harvard. These are only rough estimates 

 but they may serve as a first approximation for deducing the value of il/. In the 

 following table the clusters are grouped according to the apparent diameter. The 

 first column gives the limits of the diameter, the second column the mean diameter, 

 the third the number of clusters in each group, the fourth column the mean distance 

 — r — supposing 



where d denotes the mean distance. The fifth column gives the mean apparent 

 magnitude of the brightest stars in the clusters of each group. The last column 

 gives the corresponding value of the mean absolute magnitude. 



TABLE 3. 





Limits of 



Mean 



Number 



Mean 







diameter 



diameter 



distance 



m 



M 



(K 5' 



3.1b 



24 



42.7 



14.1 



6.0 



5' <rf< 10' 



8.50 



12 



18.9 



13.1 



6.7 



lO'<:rZ<15' 



13 3 



9 



12.0 



13.0 



7.6 



15' < d 



25.6 



5 



6.2 



12.0 



8.0 



It is a marked increase in 31 with decreasing distance. This increase is pro- 

 bably only accidental, which I conclude from the fact that the change in 31 with 

 increasing value of the distance is in inverse order, if the values of m are taken 

 not from the photographic magnitudes of Bailey but from the visual magnitudes 

 in Dreyer's N. G. C. 



The mean absolute magnitude of the considered cluster stars is 7.1. 



For realizing the bearing of this result I remined of some facts regarding the 

 absolute magnitudes of the stars. 



The absolute magnitude of a star is different for stars of different spectral 

 types, but even stars of the same spectral type (or subtype) may have very different 



5 



