PROGRESS OF MODERN ASTRONOMY 



" 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 conditions were fulfilled, it 

 could scarcely last long, and, if it did, the immense pre- 

 ponderance of one side of the ring would be easily ob- 

 served, 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 around it in the 

 form of waves, and will not introduce dangerous con- 

 fusion. If the satellites are unequal, the propaga- 

 tions of the waves will no longer be regular, but dis- 

 turbances 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 a cloud of evenly distributed uncon- 

 nected 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. Suppos- 

 ing 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 con- 

 sist of disconnected particles; these must be either 



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