132 SEE— DYNAMICAL THEORY [April 19, 



able, and the images spread somewhat on the plate, it is possible 

 that longer photographic exposures or better plates, on which the 

 images do not spread, would give relatively more stars in the region 

 of the middle of the radius of the cluster, and thus bring the law 

 of density for clusters into essential agreement with the monatomic 

 law of density. 



Further photographic observations, with the best modern instru- 

 ments, alone would decide this question. A final decision can not 

 be made yet, but in order to have the judgment of the best con- 

 temporary astronomical photographer on the subject, I have recently 

 referred the question to Professor W. S. Adams, acting director 

 of the solar observatory at Pasadena, who reports as follows: 



" I regret that I cannot give answers which would be at all conclusive to 

 your questions regarding the distribution of the fainter stars in star clusters. 

 Up to the present time only a few counts have been made upon our photo- 

 graphs. So far as these go, they do not appear to show any tendency on the 

 part of the fainter stars to predominate around any particular portion of the 

 radius of the cluster, but rather for the distribution to be tolerably uniform. 

 The problem is made difficult by the fact that the central part of our photo- 

 graphs is almost always burned out, so that counting is impossible for some 

 distance along the radius. We have begun, however, to take series of photo- 

 graphs of clusters, giving exposure times with a ratio of i to 2.5. These 

 should help greatly in providing an answer to your questions." 



On the whole the indications are that the capturing process of 

 drawing in stars from without is still going on. This would ac- 

 count for the small density near the outside of the cluster, and also 

 the great central density, the latter being an accumulative effect of 

 the various shells in the course of millions of ages. 



V. The Potential due to a Mass of Globular Figure 

 Assumed under the Action of Central Powders. 



In my "Researches," \"ol. II., 1910, I have outlined the process 

 by which the nebulse form by the aggregation of dust from a dis- 

 tance; and shown that the collecting streams may often take the 

 spiral form, and in this early stage are not of symmetrical figure. 

 The general integrals in Section II. are required to express the at- 

 traction of these unsymmetrical masses. But in true sidereal sys- 

 tems as old and fully developed as the globular clusters are known 



