120 ON THE RINGS OF SATURN. 



If a further diminution of width is attempted, a difficulty is encountered in the width 

 of the intervals. 



In the last case supposed, the area occupied by the intervals is already double the 

 limit previously assigned. If we lessen the space occupied by the intervals, by bringing 

 the adjacent rings nearer together, / decreases instead of increasing. 



But there are still stronger objections to a large number of small rings near to each 

 other. 



It is known in the case of a single ring, that, if it were perfectly uniform in every 

 part of its circumference, the slightest exterior disturbance would precipitate it upon the 

 body of the planet. To avoid this catastrophe, we must suppose each ring to be an ir- 

 regular solid, its centre of gravity not coinciding with its centre of figure, but having a 

 motion of rotation about the body of Saturn. In addition to this, a number of regular 

 concentric rings are in a position of unstable equilibrium, by virtue of their own mutual 

 attractions. The slightest inequality in the intervals would have the effect of throwing 

 the whole system into confusion. 



Let us suppose, for instance, that the inner ring deviate by ever so small an amount 

 from an exact central position with reference to the ring outside of it. The nearest sides 

 commence moving together, until they come in contact. All the others must follow. 

 The consequence of such a conflict of these masses, each urged by different velocities, 

 corresponding to the different times of rotation of the several rings, must be fatal to the 

 whole structure. It is therefore again necessary that the rings be not of regular figure 

 or density. 



But if these irregularities are small, there will be only a feeble resistance opposed to 

 their tendency to fell upon the body of the planet. On the other hand, if they be large, 

 they will become the source of mutual disturbances, which must end in their destruction, 

 by causing them to fall upon each other. The smallness of the intervals between them, 

 and the near equality in the period of rotation of two adjacent rings, will make the 

 danger of the latter event imminent, if not wholly unavoidable. The nearness of the 

 rings will in any case render it impossible that they can assume a figure of equilibrium 

 permanent or nearly so. 



The hypothesis that the whole ring is in a fluid state, or at least does not cohere 

 strongly, presents fewer difficulties. 



There being no longer an unyielding coherence between the particles of the inner 

 and outer edges, they have not necessarily the same jieriod of rotation about Saturn. A 

 continual flow of the inner particles past the outer may be supposed, by which the cen- 

 trifugal force will be brought into equilibrium with the other forces. And even should 



