1912.] OF THE GLOBULAR CLUSTERS. 151 



bution of dust, out of which the ckisters and nebulae are finally built. 

 Moreover, as already remarked, this general argument, drawn from 

 the sidereal universe as a whole, is minutely verified in the construc- 

 tion of clusters, by the exact equality of thousands of closely asso- 

 ciated stars, which thus supply a criterion of unrivaled rigor. This 

 cluster criterion authorizes the conclusion that the theory may now 

 be removed from the category of speculation and entered in the list 

 of established facts relating to the physical universe. The most 

 obvious indications of nature are plain enough ; and in interpreting 

 them all we need to do is to follow the theory of probability, which, 

 as Laplace has remarked, is nothing but common sense reduced to 

 calculation. This theory tells us that there is a deep underlying 

 cause for the perfect equality of the associated stars in clusters, 

 which can be nothing else than the mutual interaction of attractive 

 and repulsive forces in these island universes. 



XIIL The Real Dimensions of the Clusters and the Average 

 Distances of the Stars Apart. 



The question of the distances of the clusters is one which at 

 present cannot be fully answered, owing to the lack of certain obser- 

 vational data; but it is well known that nearly all these masses of 

 stars are very remote. To be sure such an outspread swarm as 

 Coma Berenices, really is a cluster so near us as not to be suspected 

 of belonging to the same type as the better defined Pleiades, Praesepe 

 and Omega Centauri. But leaving out of account a few exceptions 

 of this class we may say that the globular clusters in general, like 

 the nebulae considered by Dr. Max Wolf in A. N., 4549, are thou- 

 sands of light-years in diameter. This is proved by the comparative 

 faintness of the component stars, and the large angular magnitude 

 of the clusters as seen in the sky. 



Accordinglv, even when there are thousands of stars in a verv 

 compressed cluster, they are not really close together, but separated 

 by great intervals, of the order of a light-year. Thus the components 

 in a dense cluster probably are somewhat closer together than our 

 sun is to Alpha Centauri ; and yet the intervals can hardly be less 

 than a ten thousand fold radius of the earth's orbit, the light-year 



