4 6o SCIENCE PROGRESS 



will satisfy the necessary conditions of a steady state with a 

 random velocity distribution and with a limiting velocity 

 equal to the velocity of escape. Other considerations are 

 examined, but the general conclusion is that no obvious theo- 

 retical explanation can be found for the observed law. 



J. H. Jeans, M.N., R.A.S., lxxvi. p. 567, 1916, has handled 

 the same problem but in a different way. Jeans had already 

 shown that a cluster of stars, free from external influences, 

 can only be in a steady state provided (1) that there is star- 

 streaming, and that the figure is not necessarily spherical, or 

 (2) that there is no star-streaming, when the figure must be 

 spherical. Taking this latter case, a general law is obtained 

 for the density, depending upon the form assumed for the 

 gravitational potential. Under special assumptions this law 

 is found to reduce to Plummer's law, but these assumptions 

 are artificial in nature and such as to lead to a divergence at 

 the centre and edges of the cluster, at the places in fact where 

 Plummer's law gives the worst agreement. Jeans finds that, 

 in general, at the outer edges the law of density should be 

 p = kr~ i , which appears to agree with the counts better than 

 does Plummer's formula. Beyond that it does not seem 

 possible to pick out any definite features common to all clusters 

 in the law of distribution ; the law depends upon a number 

 of constants and there is no reason why these should be given 

 arbitrary values. 



H. Shapley, Observatory, xxxix. p. 452, 1916, who has 

 gathered much observational material in connection with 

 globular clusters, discusses the counts from which Plummer and 

 von Zeipel have deduced their density law and raises two 

 queries in regard to them, viz. (1) are the stars counted 

 sufficiently representative to give even a rough indication of 

 the structure of the whole cluster, and (2) do the counts give 

 the true distribution of the stars brighter than a definite 

 magnitude ? Photographs taken with the large 60-inch 

 reflector at Mount Wilson have established the two following 

 facts : (1) that there is a large range between the extremes 

 of brightness of the stars in the clusters, probably not less than 

 ten magnitudes at least, and (2) that as the magnitude decreases 

 there is a corresponding decrease in the colour index. These 

 results mean that in the counts which have so far been made 

 the brightest stars only have been counted, which probably 



