Hotatory Motion, the Gyroscope, tj-c. 157 



ill the case of Saturn's ring the centre of attraction is supposed to be 

 in the plane of the ring, and must tend to move it in its plane. The 

 attraction cannot tend to alter the plane of motion of the ring unless 

 something exists to cause the ring to move about an external centre in 

 the prolongation of its axis, as in the case of the model, and then it 

 would move conically. Mr. Elliot admits that if Saturn's ring did not 

 rotate, it would move in its own plane towards the centre of attraction. 

 Supposing it solid and free to do this, Mr. Elliot's reasoning, if applied 

 to the case of an unsupported disc rotating on a horizontal axis, would 

 seem to prove that the action of gravity ought not to make the disc 

 fall, Mr. Elliot says that Laplace omitted the rotation of the ring 

 when calculating the attractive force upon it ; but if the ring is solid 

 and uniform, that rotation could not affect the result of the calculation 

 in the sHghtest degree. 



Mr. Elliot's remarks on the stability of Saturn's rings led me to con- 

 sider the subject a little, but I have not been able to solve the problem. 

 I cannot, however, conceive any way of accounting for their stability 

 unless they are in a state of greater or less fluidity. If the rings are 

 solid, their mere rotation cannot give them stability, and Laplace has 

 demonstrated that they have no stability without the rotation. If 

 they are fluid, however, the parts nearer the centre of attraction will 

 move with increased velocity, and will have a greater centrifugal force 

 than the more distant pai-ts; whilst the latter, from their smaller 

 velocity, will be accumulated in such a way that the section of the 

 ring fiui;hest from the centre of attraction will be greater than the 

 opposite and nearest section ; so that whilst the cohesion of the parts 

 may prevent sufiicient increase in the velocity and centrifugal force of 

 the parts nearest the centre of attraction to prevent the ring from 

 moving towards that centre, the preponderance of matter on the oppo- 

 site side of the ring wiU cause the insuflBcient corrective force to be 

 supplemented by the consequent increase of the attraction on the farthest 

 side of the ring.* 



December 16, 1857. — The Phesident in the Chair. 



The Hon. Andrew Galbraith, Lord Provost of the City, was admitted 

 a member of the Society. 



* I gave the above idea as a mere suggestion ; it would require a difficult anal3'tical 

 calculation to determine whether the stability could be maintained in the way I have 

 imagined. After my paper was read, I was informed that Professor Clerk Maxwell had 

 solved the problem on the supposition that the rings consisted of perfectly independent 

 particles. I have not, however, yfl liecn able to see his solution. — E. IT., January, 1868. 



