191^.] OF THE GLOBULAR CLUSTERS. 149 



to produce nebulae in the vacant regions of the heavens ; and this 

 concentration of the large masses under gravity, and the redistri- 

 bution of the fine dust by the action of repulsive forces is the great 

 law of nature which preserves the order of the starry heavens. 



XII. The Mutual Interaction of Attractive and Repulsive 



Forces Confirmed by a Delicate Criterion Based on 



the Exact Equality of Thousands of Associated 



Stars in a Cluster. 



Elementary considerations on the principles of probability will 

 show that the chances of even two associated stars being of equal 

 brightness is slight ; it is still smaller for three, four and higher 

 multiples, and when the number becomes large the probability of the 

 chance association of such equal stars totally disappears. Accord- 

 ingly, it is not by accident that thousands of stars observed in a 

 cluster, with perfectly symmetrical accumulation towards the center 

 of the associated stars, all known to be at nearly the same distance 

 from us, are as exactly equal in every respect as the finest coins 

 turned out of a mint. There must be in nature a reliable process 

 for the manufacture of these nearly equal stars, which is described 

 above for the first time. 



To prove this more conclusively we may compare clusters with 

 double and multiple stars, which are systems of lower order. In 

 binaries the components often are very unequal in brightness, and 

 also in mass. The same principle, as is well known, holds for triple 

 and quadruple stars. Now in these double and multiple star systems 

 the ratio of the mass of the components depends on the chance 

 division of the original nebulosity gathered from the heavens, not 

 from the associated stars themselves; but in the clusters the principle 

 of redistribution becomes largely predominant, owing to the great 

 number of radiating centers in close association. It is not surpris- 

 ing, therefore, that the lower orders of stellar systems should in- 

 clude : first, single stars, with planetary systems, amounting to about 

 four fifths of all the stars; second, binary stars, with unequal com- 

 ponents ; third, multiple stars, also with components very unequal. 

 This inequality of the associated stars is to be expected in all sidereal 



PROC. AMER. PHIL. SOC, LI. 204 G, PRINTED JUNE 6, I9I2. 



