130 T. C. CHAM BERLIN 



control of the stellar galaxy. The sphere of control of the atom 

 enters into the sphere of control of the molecule, and that into 

 higher orders in succession up to the earth and beyond. The 

 whole cosmic scheme seems to be a system of such hierarchies 

 whose limits in either direction are unknown. 



III. The dynamic value of each sphere of control dies rapidly 

 away from the mass in which it centers to its outer border. Not 

 only this, but each sphere of control that revolves within a superior 

 sphere of control is larger or smaller, more effective or less effective, 

 according to its position within such superior sphere of control. 

 It is likely to be either increasing or diminishing as the body in 

 which it centers swings through its orbit. If it were made to 

 constantly approach the controlling body, its extent and efficiency 

 of control would grade entirely away to extinction before such 

 superior mass was reached. 



IV. In such spheres of control as center in single great masses, 

 the differential pull of the controlling mass becomes so great 

 relatively, in its innermost portion, that bodies of a minor order 

 intruding upon it are liable to be disrupted. When the approaching 

 minor bodies are gaseous, their spontaneous tendency to dis- 

 persion insures their dissipation. When they are solid, the degree 

 of fragmentation to which they are subject is likely to be limited to 

 certain sizes, for as the fragments grow small the strength of their 

 cohesion increases relative to their mass. Cohesion is not likely 

 to be important in large bodies because they are usually self- 

 compressed and hot within to such a degree that their tendencies to 

 expand, when pressure is relieved, usually surpass their coherence. 



The outer border of the disruptive zone is known as the Roche 

 limit. Its determination by Roche was based on an ideal homo- 

 geneous fluid satellite approaching an ideal homogeneous fluid 

 planet of equal uniform density, cohesion being neglected. He 

 fixed the limit of disruption at 2 .44 times the radius of the planet.^ 

 This limit is in close accordance with what seems to be the realized 

 result in the case of Saturn's rings which stand as the classic ex- 

 ample of minute division and distribution in response to this dis- 

 ruptive effect. The mathematical conclusions of Roche were amply 



^ Edward Roche, Memoirs de l' Academic Montpelier, I, p. 243. 



