374 ON THE STABILITY OF THE MOTION OF SATURN'S RINGS. 



most distinct, seems to indicate that the approach towards the planet is less 

 rapid near the edge, as we had reason to conjecture. As to the apparent 

 unchangeableness of the exterior diameter of the outer ring, we must remember 

 that the outer rings are certainly far more dense than the inner one, and that 

 a small change in the outer rings must balance a great change in the inner 

 one. It is possible, however, that some of the observed changes may be due 

 to the existence of a resisting medium. If the changes already suspected should 

 be confirmed by repeated observations with the same instruments, it will be 

 worth while to investigate more carefully whether Saturn's Rings are permanent 

 or transitionary elements of the Solar System, and whether in that part of 

 the heavens we see celestial immutability, or terrestrial corruption and generation, 

 and the old order giving place to new before our own eyes. 



APPENDIX. 



On the Stability of the Steady Motion of a Rigid Body about a Fixed Centre of Force. 

 By PROFESSOR W. THOMSON (communicated in a letter). 



THE body will be supposed to be symmetrical on the two sides of a certain plane 

 containing the centre of force, and no motion except that of parts of the body parallel 

 to the plane will be considered. Taking it as the plane of construction, let G (fig. 14) 

 be the centre of gravity of the body, and a point at which the resultant attraction of 

 the body is in the line OG towards G. Then if the body be placed with coinciding 

 with the centre of force, and set in a state of rotation about that point as an axis, with 



an angular velocity equal to A/ \r> (where / denotes the attraction of the body on a 



unit of matter at 0, S the amount of matter in the central body, M. the mass of the 

 revolving body, and a the distance OG), it will continue, provided it be perfectly undis- 

 turbed, to revolve uniformly at this rate, and the attraction Sf on the moving body will 

 be constantly balanced by the centrifugal force ufaM of its motion. 



Let us now suppose the motion to be slightly disturbed, and let it be required to 

 investigate the consequences. Let X, S, Y, be rectangular axes of reference revolving 

 uniformly with the angular velocity o>, round S, the fixed attracting point. Let x, y, be 

 the co-ordinates of G with reference to these axes, and let XS, YS denote the components 



