ON THE STABILITY OF THE MOTION OP SATURN'S RINGS. 295 



heavy satellite about 4-$- times tlie weight of the ring, but this load, besides 

 being inconsistent with the observed appearance of the rings, must be far too 

 artificially adjusted to agree with the natural arrangements observed elsewhere, 

 for a very small error in excess or defect would render the ring again unstable. 



We are therefore constrained to abandon the theory of a solid ring, and 

 to consider the case of a ring, the parts of which are not rigidly connected, 

 as in the case of a ring of independent satellites, or a fluid ring. 



There is now no danger of the whole ring or any part of it being pre- 

 cipitated on the body of the planet. Every particle of the ring is now to be 

 regarded as a satellite of Saturn, disturbed by the attraction of a ring of 

 satellites at the same mean distance from the planet, each of which however is 

 subject to slight displacements. The mutual action of the parts of the ring will 

 be so small compared with the attraction of the planet, 'that no part of the 

 ring can ever cease to move round Saturn as a satellite. 



But the question now before us is altogether different from that relating to 

 the solid ring. We have now to take account of variations in the form and 

 arrangement of the parts of the ring, as well as its motion as a whole, and 

 we have as yet no security that these variations may not accumulate till the 

 ring entirely loses its original form, and collapses into one or more satellites, 

 circulating round Saturn. In fact such a result is one of the leading doctrines 

 of the " nebular theory " of the formation of planetary systems : and we are 

 familiar with the actual breaking up of fluid rings under the action of "capil- 

 lary" force, in the beautiful experiments of M. Plateau. 



In this essay I have shewn that such a destructive tendency actually exists, 

 but that by the revolution of the ring it is converted into the condition of 

 dynamical stability. As the scientific interest of Saturn's Rings depends at 

 present mainly on this question of their stability, I have considered their motion 

 rather as an illustration of general principles, than as a subject for elaborate 

 calculation, and therefore I have confined myself to those parts of the subject 

 which bear upon the question of the permanence of a given form of motion. 



There is a very general and very important problem in Dynamics, the solu- 

 tion of which would contain all the results of this Essay and a great deal 

 more. It is this 



"Having found a particular solution of the equations of motion of any 

 material system, to determine whether a slight disturbance of the motion indi- 



