Abstract
If Saturn's rings were several particles thick the damping effect of collisions on the inclinations and eccentricities would reduce the rings in less than a year to a state where the particles were piled one on another. Dissipation by friction and impact would not cease at this stage. Its later effects would extend the ring inwards and outwards in its own plane, until it was nowhere more than one particle thick and the spacing was just enough for collisions to be avoided. The time needed to attain this state is estimated to be of the order of 10 6 years for particles of diameter 1 cm. and less for larger ones. Some comments are made on Maxwell's and Goldsbrough's criteria for stability.

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