T9I2.] OF THE GLOBULAR CLUSTERS. 161 



for the spectroscopic binaries; and the law of formation is the same 

 for all the double stars as for the planets of the solar system, where 

 Babinet's criterion is absolutely decisive against the detachment 

 theory generally held since the days of Laplace, but now universally 

 abandoned. 



Summary and Conclusions. 



Without attempting in this closing summary to recapitulate the 

 contents of this memoir in detail, it may yet be well to draw attention 

 to some of the most significant conclusions at which we have arrived. 



1. As intimated in the first section of this paper the problem of 

 ■w-bodies, under ideal dynamical conditions, remains forever beyond 

 thepower of the most general methods of analysis; but the dynamical 

 theory of clusters gives us the one secular solution of this problem 

 found under actual conditions in nature. For when ii is of the order 

 of 1,000, so as to give rise to a cluster, the clustering power observed 

 by Herschel operates to exhaust the mutual potential energy of the 

 system, and bring about increasing accumulation in the center, so 

 that the cluster finally unites into a single mass of enormous magni- 

 tude. Probably the giant stars of the type of Canopus and Arcturus 

 have arisen in this way. 



2. And since attendant bodies of every class — as satellites, planets, 

 comets, double and multiple stars — tend everywhere to approach the 

 centers about which they revolve, as an inevitable effect of the growth 

 of the central masses and of the action of the resisting medium over 

 long ages, it follows that the secular solution of the problem of clus- 

 ters is more or less valid for all cosmical systems. They finally end 

 by the absorption of the attendant bodies in the central masses which 

 now govern their motions. 



3. The dynamical theory of globular clusters shows that the clus- 

 tering power inferred by Herschel is nothing else than the action of 

 universal gravitation ; and that it operates on all sidereal systems, but 

 does not produce the cumulative effect which Herschel ascribed to 

 the ravages of time inside of millions of ages. 



4. The globular clusters are formed by the gathering together of 

 stars and elements of nebulosity from all directions in space; and 



