152 SEE— DYNAMICAL THEORY [April 19, 



being 63,275 times that distance. In fact the average distances are 

 likely to be several light-years, and thus of the order 100,000 radii 

 of the earth's orl)it. 



This great distance of the stars apart, even in the densest cluster, 

 will enal)le us to realize the well-known fact that our sun is in a 

 solar cluster, which includes Sirius, the stars of Ursa Major, and 

 many other bright objects. It also enables us to appreciate why the 

 motion in the clusters necessarily is slow, owing to the great inter- 

 vening spaces and the feebleness of the disturbing forces acting on 

 the individual stars. And at the same time we easily see why such 

 a system, under the mutual gravitation of its parts, might survive 

 for infinite ages, without sensible decay of its order or stability. 

 Newcomb therefore was right when he remarked that there might 

 be planets revolving about the stars in a cluster (article " Stars," 

 Encyclopedia Americana) ; for we ourselves live on a planet attached 

 to a star of the solar cluster, and the other clusters of the sidereal 

 universe are not very different from that including our sun. 



Sir William Herschel was of the opinion (Phil. Trans., 1789, p. 

 225) that the clusters which are most compressed are drawing on 

 towards a period of dissolution. In an earlier paper of 1785 Her- 

 schel suggested that the clusters are the laboratories of the universe 

 where the most salutary remedies for the decay of the whole are 

 prepared (Phil. Trans., 1785, p. 217). 



In my "Researches," \"ol. II., 1910, I have independently pointed 

 out that the condensation of very compressed clusters into one mass 

 is the only logical explanation of such immense stars as Canopus and 

 Arcturus. For it appears that with the advance of age the state of 

 compression slowly increases, and when it has become extreme, and 

 all the single bodies are drawn very near the center, it is quite likely 

 that the cluster by conflagration may become the furnace of a labo- 

 ratory of the universe for repairing through repulsive forces the 

 ravages wrought by universal gravitation in the course of millions 

 of ages. 



If this be true someone may ask why we do not find some cluster 

 in the stage of conflagration? But if we recall that only a little 

 over one hundred globular clusters are known, with their internal 



