372 T. C. CHAMBERLIN 



removed, its internal elasticity would disrupt its exterior with 

 much violence; and if the gravitative stresses were more grad- 

 ually removed, the disruption would still be complete and per- 

 vasive, though less violent. How far a similar view may be 

 entertained with reference to small bodies like the asteroids is 

 uncertain, but even in these it is not improbable that the internal 

 elastic factors would offset in some large part, if not entirely, 

 the restraining force of the general cohesion of the mass. 



From these considerations it would seem that the sphere of 

 disruption, even in solid bodies of the nature of satellites and 

 asteroids, may closely approximate to the theoretical Roche 

 limit, while, for large bodies intensely compressed and very hot 

 within, the practical sphere of disruption might actually exceed 

 the Roche sphere. In the case, of large gaseous bodies like 

 the sun, intensely heated and compressed in the central por- 

 tions, the disruptive or dispersive sphere must be much larger 

 than the Roche sphere. But of this later. For the smaller 

 solid bodies, and for present purposes, it may be assumed 

 that the sphere of disruption is practically defined by Roche's 

 limit. 



The size of the sphere of disruption compared with the size 

 of the body producing the disruption is an essential point in this 

 discussion. The relative magnitude of these varies for every 

 couplet of bodies brought under consideration, because it is 

 dependent on density, cohesion, internal elasticity, and other 

 varying factors. Roche has shown that, if the two bodies are 

 incompressible fluids of the same density, and without cohesion, 

 the limit of disruption is 2.44 times the radius of the body 

 producing the disruption. The cross section of this body will 

 therefore be to the cross section of the Roche sphere as i is to 

 5.95. The disk of the outer ring of Saturn, compared with that 

 of the planet, whose density is unusually low, is a trifle below 

 this ratio (1:5.29), but may be. taken as a practical sanction of 

 the figure theoretically deduced. The disk of the Earth, a dense 

 body, is to the disk of the Roche limit, as computed by Darwin, 

 as I to 7.5. It may therefore be concluded that where planets 



