DYNAMICAL THEORY OF THE GLOBULAR CLUSTERS 



AND OF THE CLUSTERING POWER INFERRED BY 



HERSCHEL FROM THE OBSERVED FIGURES 



OF SIDEREAL SYSTEMS OF HIGH ORDER. 



By T. J. J. SEE. 

 (Read April /p, 1012.) 



(Plates VIII (bis) and IX.) 



I. Introductory Remarks. 



More than a century and a quarter have elapsed since it was con- 

 fidently announced by Sir William Herschel that sidereal systems 

 made up of thousands of stars exhibit the effects of a clustering 

 power which is everywhere moulding these systems into sym- 

 metrical figures, as if by the continued action of central forces 

 (Phil. Trans., 1785, p. 255, and 1789, pp. 218-226). In support of 

 this view he cited especially the figures of the planetary nebulae, 

 and the globular clusters, as well as the more expanded and irregular 

 swarms and clouds of stars visible to the naked eye along the course 

 of the Alilky Way, which thus appears to traverse the heavens as a 

 clustering stream. And yet notwithstanding the early date of this 

 announcement and the unrivaled eminence of Herschel, it is only 

 very recently that astronomers have begun to consider the origin of 

 sidereal systems of the highest order. 



The historical difficulty of solving the problem of n-bodies, when 

 n exceeds 2, which dates from the establishment of the law of 

 universal gravitation by Newton in 1687, will sufficiently account 

 for the restriction of the researches of mathematicians to the plane- 

 tary system, where the central masses always are very predominant, 

 the orbits almost circular and nearly in a common plane, and to other 

 simple systems such as the double and multiple stars : but owing to 

 the general prevalence of the clustering tendency pointed out by 

 Herschel and now found to be at work throughout the sidereal uni- 



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