336 ON THE STABILITY OF THE MOTION OF SATURN'S RINGS. 



20. We now pass to the case of a ring of an entirely different construc- 

 tion. It is possible to conceive of a quantity of matter, either solid or liquid, 

 not collected into a continuous mass, but scattered thinly over a great extent 

 of space, and having its motion regulated by the gravitation of its parts to 

 each other, or towards some dominant body. A shower of rain, hail, or cinders 

 is a familiar illustration of a number of unconnected particles in motion ; the 

 visible stars, the milky way, and the resolved nebulae, give us instances of a 

 similar scattering of bodies on a larger scale. In the terrestrial instances we 

 see the motion plainly, but it is governed by the attraction of the earth, and 

 retarded by the resistance of the air, so that the mutual attraction of the 

 parts is completely masked. In the celestial cases the distances are so enor- 

 mous, and the time during which they have been observed so short, that we 

 can perceive no motion at all. Still we are perfectly able to conceive of ;i 

 collection of particles of small size compared with the distances between them, 

 acting upon one another only by the attraction of gravitation, and revolving 

 round a central body. The average density of such a system may be smaller 

 than that of the rarest gas, while the particles themselves may be of great 

 density ; and the appearance from a distance will be that of a cloud of vapour, 

 with this difference, that as the space between the particles is empty, the rays 

 of light will pass through the system without being refracted, as they would 

 have been if the system had been gaseous. 



Such a system will have an average density which may be greater in some 

 places than others. The resultant attraction will be towards places of greater 

 average density, and thus the density of those places will be increased so us 

 to increase the irregularities of density. The system will therefore be statically 

 unstable, and nothing but motion of some kind can prevent the particles from 

 forming agglomerations, and these uniting, till all are reduced to one solid 

 mass. 



We have already seen how dynamical stability can exist where there is 

 statical instability in the case of a row of particles revolving round a central 

 body. Let us now conceive a cloud of particles forming a ring of nearly uni- 

 form density revolving about a central body. There will be a primary effect of 

 inequalities in density tending to draw particles towards the denser parts of the 

 ring, and this will elicit a secondary effect, due to the motion of revolution, 

 tending in the contrary direction, BO as to restore the rings to uniformity. The 



