250-252] Globular Star-Clusters 243 



whole, and consequently their original motions persist to a much greater 

 extent than is the case with other types of stars. Thus they still lie mainly 

 in the galactic plane in which they were born ; they are still, perhaps, ex- 

 panding in this plane ; to a large extent they still move in undissipated star- 

 clusters, perhaps even carrying wisps of uncondensed nebulous~fnatter along 

 with them. 



Although some such conjecture naturally suggests itself, it has to be ad- 

 mitted that the subject is full of difficulty. No single hypothesis seems able 

 to explain all the facts ; for the present, apparently, we m'ust be content to 

 hold a number of self-contradictory hypotheses. Each of these hypotheses 

 can, perhaps, give us a glimpse of part of the truth, but the time for welding 

 them into one consistent whole has not yet come. 



GLOBULAR STAR-CLUSTERS 



252. Even the roughest of calculations makes it clear that the dimensions 

 of globular clusters are much less than those of our galactic universe, while 

 their star-density is vastly higher. Shapley* has made a special study of the 

 bright cluster M3 (N. G. C. 5272) in Canes Venatici. He estimates its 

 parallax to be OO00074" with an error of less than 20 per cent. ; it follows 

 that the majority of the stars in the cluster are included within a sphere of 

 10 parsecs radius. Shapley estimates that such a sphere will contain at least 

 15,000 stars brighter than magnitude 20. Each of these stars is at least two 

 absolute magnitudes brighter than the sun. 



Now in a sphere of the same radius surrounding our sun there are at most 

 five stars of absolute magnitude two degrees brighter than the sun. As 

 regards stars of this brightness, the stellar density in the cluster is 3000 times 

 greater than that in the neighbourhood of our sun. We are not entitled to 

 make a similar statement for stars of all kinds, but may notice that the 

 stellar density of these bright stars in the cluster is far higher than our 

 estimated stellar density for stars of all kinds in our galactic universe. The 

 density of these bright stars in the cluster is about four per cubic parsec, as 

 against our estimate of one per 13 cubic parsecs for stars of all kinds in our 

 galactic universe. 



Thus as regards stellar density the condition of this cluster approximates 

 more closely to the earlier condition we have imagined for our universe than 

 to its present condition, and the same is readily seen to be true for other 

 clusters. To examine the effect on our calculations as to collision-frequency, 

 etc., let us suppose the stellar density to be 1000 times greater than that 

 assumed for our universe in 223. Assuming the stars to be of diameter 

 equal to that of Neptune's orbit we find that a star would experience material 



* Astron. Soc. Pacific, No. 172 (1917) ; a later study of this and other star -clusters will be found 

 in Mt Wilson Contributions, No. 152. 



162 



