164 SEE— DYNAMICAL THEORY [April 19. 



13. As sidereal systems of lower order are conserved by projec- 

 tile forces, it is probable that the clusters likewise' have a spiral 

 motion of rotation, with similar projectile forces tending to counter- 

 act simple progressive collapse. The period of the orbital revolution 

 of the stars of a cluster is found to be common to all, without regard 

 to the dimensions of the elliptical orbits described, and thus the 

 whole system may have a common period of oscillation, after wdiich 

 the initial condition is perfectly restored. This possibility in the 

 dynamics of a cluster is exceedingly wonderful, and results from the 

 central attraction depending directly on the distance. 



14. The equality of brightness in star clusters shows that some 

 process of compensation between the attractive and repulsive forces 

 has produced stars of wonderful uniformity of luster. Thus the 

 present investigation confirms the previous researches on the evolu- 

 tion of the stellar systems, which have laid the foundations for a new 

 science of the starry heavens. 



15. Accordingly the capture theory of cosmical evolution being 

 now firmly established for the clusters, where the nature of the 

 process is entirely clear, it becomes at once a guide to us in dealing 

 with systems of lower order ; and we see that the law of nature is 

 uniform and everywhere the same, the large bodies working in 

 towards the centers of attraction, while the only throwing off that 

 ever takes place is of small particles driven out of the stars by the 

 action of repulsive forces. All planetary bodies are formed in the 

 distance, and have their orbits reduced in size by increase of the 

 central masses, and rounded up by moving in a resisting medium. 

 This is a perfectly general law of the sidereal universe. It verifies 

 the early conjectures of Plato and Nezvton as to the stability of the 

 order of the world, and shoics that these ilhistrious philosophers 

 were quite justified in concluding that the Deity alzi'ays geometrizes. 

 The spiral nebulae tend to develop systems with rounder and rounder 

 orbits, and the clusters made up of thousands of stars assume 

 globular figures with minimal surfaces and internal density so 

 arranged as to give maximum exhaustion of the potential energy. 



16. This is geometry of the most marvellous kind, as we find it 

 impressed on the systems of the sidereal universe ; and the perfection 



