146 SEE— DYNAMICAL THEORY [April 19, 



periods, and aphelia near Jupiter's path ; and those which still over- 

 lap his orbit are being gradually worked into the more stable region 

 within the orbit of that giant planet. In the same way the asteroids 

 have been thrown within Jupiter's orbit, as H. A. Newton justly 

 remarked in 1894 (cf. my "Researches," \^ol. II., 1910, p. 699), 

 by a process which Professor E. W. Brown has more fully investi- 

 gated in the Monthly Notices for March, 191 1. Professor H. A. 

 Newton's researches and those of Callandreau and Tisserand on 

 the capture of comets are well known, and need not be described 

 here. 



Now if for Jupiter we substitute the action of the shell of the 

 cluster, it may be thought that Jupiter is a very large mass, while 

 the comets are very small ; whereas the stars in the shell of the 

 clusters are not supposed to be so much larger than the star 

 falling in. This is ver}' true, but as the shell contains many stars 

 in mutual adjustment to an average state of stability, the oscillating 

 star in the course of ages will be disturbed by the many stars, and 

 the cumulative effects will be added together, just as the actions on 

 comets are by the massive planet Jupiter. The mass of the shell 

 greatly exceeds that of the single oscillating star, and even if some of 

 the individual stars in the shell are considerably disturbed, yet the 

 disturbance in successive revolutions will not effect the same stars, 

 owing to movements within the shell of the cluster; and thus in 

 the long run the only possible effect of the action of the many 

 upon the one visiting star will be to dampen its energy of oscillation, 

 till it too will have its path reduced and take its place in the shell 

 with the original group. Thus the visitor from without is entrapped 

 and its movements dragged down to the dead level of the rest of the 

 stars in the shell. 



This is a general explanation of the capture process established 

 by the more rigorous method of integration depending on Green's 

 theorem, when some of the terms become infinite. It seemed desir- 

 able to examine the matter from both points of view. 



To be sure this transformation may take many millions of years, 

 but the average effect of the action of the shell in the long run is 

 certain. As the stars in the shell are comparatively quiescent, the 



