372 ON THE STABILITY OF THE MOTION OF SATURN 8 KINGS. 



is known that none of the other rings have expanded, then the cause of the 

 change cannot be the mutual action of the parts of the system, but the resistance 

 of some medium in which the rings revolve. 31- 



There is another cause which would gradually act upon a broad fluid ring 

 of which the parts revolve each with the angular velocity due to its distance 

 from the planet, namely, the internal friction produced by the slipping of the 

 concentric rings with different angular velocities. It appears, however ( 33), 

 that the effect of fluid friction would be insensible if the motion were regular. 



Let us now gather together the conclusions we have been able to draw 

 from the mathematical theory of various kinds of conceivable rings. 



We found that the stability of the motion of a solid ring depended on 

 so delicate an adjustment, and at the same time so unsymmetrical a distribution 

 of mass, that even if the exact condition were fulfilled, it could scarcely last 

 long, and if it did, the immense preponderance of one side of the ring would 

 be easily observed, contrary to experience. These considerations, with others 

 derived from the mechanical structure of so vast a body, compel us to abandon 

 any theory of solid rings. 



We next examined the motion of a ring of equal satellites, and found that 

 if the mass of the planet is sufficient, any disturbances produced in the arrange- 

 ment of the ring will be propagated round it in the form of waves, and will not 

 introduce dangerous confusion. If the satellites are unequal, the propagation of 

 the waves will no longer be regular, but disturbances of the ring will in this, 

 as in the former case, produce only waves, and not growing confusion. Sup- 

 posing the ring to consist, not of a single row of large satellites, but of a cloud 

 of evenly distributed unconnected particles, we found that such a cloud must 

 have a very small density in order to be permanent, and that this is inconsistent 

 with its outer and inner parts moving with the same angular velocity. Supposing 

 the ring to be fluid and continuous, we found that it will be necessarily broken 

 up into small portions. 



We conclude, therefore, that the rings must consist of disconnected particles ; 

 these may be either solid or liquid, but they must be independent. The entire 

 system of rings must therefore consist either of a series of many concentric rings, 

 each moving with its own velocity, and having its own systems of waves, or else 

 of a confused multitude of revolving particles, not arranged in rings, and 

 continually coming into collision with each other. 



