I9I2.] OF THE GLOBULAR CLUSTERS. 141 



shell will revolve about the common center of gravity in exactly 

 the same time as one situated near the center ; for the remoter stars 

 revolve under a greater attractive force, while the nearer ones 

 revolve under feebler forces, and all would therefore have a com- 

 mon period. The movement at the end of the period would restore 

 the cluster to its original state, the individual bodies being exactly 

 where they started from at the initial epoch. This is one of the 

 most remarkable results of the dynamics of a system of n-bodies 

 arranged in concentric shells of uniform density, depending wholly 

 on the radius, as in our typical globular clusters, which are made 

 up of stars of equal brightness and apparently of equal mass. 



If therefore the cluster were once established with such rela- 

 tions among the stars that their orbits do not intersect, and the 

 sphere of powerful attraction for each star is small compared to 

 the spaces between the neighboring stars, the wonderful system thus 

 arranged might oscillate in stability for millions of ages. These 

 conditions evidently are quite fully realized in the globular clusters, 

 as will more clearly appear from the following considerations on 

 their mode of formation. 



IX. The Symmetrical Growth of a Cluster due to a Process 



OF Internal Compensation. 



In the second volume of my " Researches," 1910, it is shown by a 

 line of argument based on the principle of continuity, similar to 

 that used by Herschel in the Phil. Trans., 181 1, p. 284, that the 

 nebulae are formed by the gathering together of dust expelled from 

 the stars under the action of repulsive forces. As this dust gathers 

 towards a center so as to form a nebula or cluster, of more or less 

 symmetrical figure, it takes a long time for the new system to acquire 

 an arrangement by which the density increases from the surface to 

 the center. In the course of ages, however, the central mass in- 

 creases or the central group of masses accumulate, by accretion of 

 dust to the individual bodies, or by the capture and redistribution 

 of interpenetrating bodies. The result, on the one hand, is that all 

 orbits will be decreased in size and the system will contract its di- 

 mensions ; and, on the other hand, this waste matter will tend to ac- 



