stellar clustors 



7 



Plotting out graphically these results taking the inverse value of the apparent 

 diameter as X-coordinate and the corresponding mean distance as ordinate we get 

 the following diagram. 



10 

 9 



8 

 7 

 6 

 5 

 4 

 3 

 2 



1 



0 1 2 3 4 5 C, 7 8 '.I in 



Fig. 1. Abscissa: inverse value of tlio apparent diameter, 

 Ordinate: corresponding mean distance. 



We find that the mean distance for small abscissae (= large apparent diameters) 

 increases proportional to the abscissae, that, however, for larger values of x the in- 

 crease of the ordinates is smaller than that of the abscissae. In the correlation table 

 we find how small apparent diameters occur at very different distances whereas 

 the array's corresponding to large apparent diameters have a small dispersion. Tills 

 accounts for the form of the regression line given in fig. 1. 



The question may be, mathematically, treated in the following way. Suppose 

 an assembly of clusters to be given and let the number of clusters between the 

 limits r ± \ dr be 



^^[r] dr. 



Assume furthermore, for simplifying our exposition, that the repartition of 

 the diameters [B) of the clusters is the same at all distances. Let 



UB) dB 



be the number of clusters having a diameter between the limits B ± \ dB. Then 



'i,[r) f,{B)drdB 



is the number of clusters at the distance r (+ | rfr) and having the diameter B (+ | dB). 

 Let b be the apparent diameter (in radians) of a cluster, then 



B = rh 



and 



(1) <Pi(r) ipal^fe) r dr db , 



denotes the number of clusters at the distance r having an apparent diameter b. 



