I9I2.] OF THE GLOBULAR CLUSTERS. 159 



At this early stage in the study of the problems of cosmogony, 

 naturally I had not exhausted the other possible modes of formation, 

 though I had largely excluded the capture of single stars by chance 

 approach due to difference in proper motion. The further study 

 of this problem has occupied a part of the past twenty years, but as it 

 has now led to the establishment of a great law of nature, one may 

 feel that the labor has not been in vain. 



From the above reasoning it will be found : 



1. That if the globes of the stars of a binary be expanded till a 

 hydrostatic connection is established between the components, the 

 fluid will thereby become so rare that no hydrostatic pressure could 

 be exerted to throw oft" a companion by rotation. 



2. A rotation rapid enough to produce such a separation could 

 not be accounted for by natural causes. 



3. Hence it is clear that the premise implying a separation by 

 rotation is false; and the true mode of formation is diametrically 

 opposite to what was long believed. Instead of being thrown oft' by 

 rapid rotation, the attendant bodies have all been formed in the dis- 

 tance, and added on from without, so that they have neared the 

 centers about which they now revolve. This uniform law greatly 

 simplifies all our conceptions of cosmical evolution. 



To illustrate the relative significance of the moments of momen- 

 tum of the axial rotations compared to the moment of momentum 

 of orbital motion, it suffices to cite the case considered in my inau- 

 gural dissertation of 1892, pp. 37-38. In this case each of the two 

 equal stars imagined expanded into a nebula has three times the mass 

 of the sun ; and the axial rotations are such as to give an oblateness of 

 2/5. The stars are set in motion at a mean distance of 30 astronomical 

 units. In the special units there adopted, it turns out that the mo- 

 ments of momentum of the axial rotations have the numerical values 

 0.394, or 0.788 for the two stars; and the moment of momentum of 

 orbital motion becomes 2.378. 



Thus with the two stars so far apart as 30, it is impossible to 

 keep the figures of equilibrium stable and yet give them rotations 

 rapid enough to render the moments of momentum of axial rota- 

 tion large compared to that of the orbital motion. Nevertheless, a 



