130 SEE— DYNAMICAL THEORY [April 19. 



Among the results cited from the researches of Pickering and 

 Bailey are these : 



1. The law of distribution is essentially the same for different 

 clusters. 



2. The bright stars and faint stars of a cluster obey the same law. 



Mr. H. C. Plummer also availed himself of the important re- 

 searches of Dr. H. von Zeipel on the cluster Messier 3 (Annales de 

 rObservatoire de Paris, Tome XXV.), in which a method was de- 

 veloped for finding the law of distribution of the stars in space, from 

 the observed law of distribution in the projection as we see it. Dr. 

 von Zeipel effected this transformation by means of a theorem due 

 to Abel. He subsequently compared his results for Messier 13 and 

 Omega Centauri with the densities to be expected in a spherical 

 mass of gas in isothermal equilibrium. 



In his paper of March, 191 1, Mr. Plummer investigates the law 

 of density for the clusters Omega Centauri, 47 Toucani, and the 

 great cluster in Hercules (M. 13). By the use of von Zeipel's 

 method he finds that in these three clusters there is a very good 

 agreement as respects the law of density. In the accompanying 

 table we give the ten points of Plummer's empirical curve of den- 

 sity, based on recent photographs. For the sake of comparison 

 we give also the corresponding points for the laws of density and 

 pressure for a sphere of gas following the monatomic law and in 

 convective equilibrium, as developed in the writer's researches on 

 the " Physical Constitution and Rigidity of the Heavenly Bodies " 

 {Astron. Nadir., Nos. 4053, 4104). The nature of these three laws 

 is best understood from the accompanying illustration. Fig. i. 



1. The cluster density is greater near the boundary, the curve 

 tending to become asymptotic, as there is no definite boundary to 

 the mass of stars. 



2. The cluster density also appears to be relatively greater near 

 the center, so that the curve intersects the monatomic curves in the 

 outer parts of the radius but again unites with them at the center, 

 after falling and pursuing a different course between the surface and 

 the center. 



3. As the apparent density of the stars in a cluster is consider- 



