378 ANNUAL OF SCIENTIFIC DISCOVERY. 



permanent, the other divisions are constantly annihilated by the 

 mutual concussion of the rings, and again re-produced by some process 

 which he does not undertake to define. This bold and ingenious theory 

 is fully sustained by my own analytical investigations, and not only do 

 my researches exhibit the possibility of this strange phenomenon, but 

 they even go farther, and, exhibiting the precise mode of action, show 

 that it must be the case of nature. If the ring had been originally 

 one, it would soon have divided itself at definite points, which can be 

 exactly computed, into portions of a determinate width. The disturb- 

 ing causes must, after a time, have driven these separate rings against 

 each other. There would then have followed an interchange and mov- 

 ing of currents, a mutual retardation, a momentary state of equilibrium, 

 as one ring and then another broke off, when the same process would 

 be again repeated. 



3. But even a fluid ring could not be permanently retained by the 

 direct action of the primary, for, whatever may be its general figure, 

 the velocity of its current must be slower at the points which are more 

 remote from the planet ; so that there must be an accumulation of fluid 

 at these points, and no exact analysis shows that the accumulation 

 precisely balances the greater distance, so that the ring must be at- 

 tracted equally in every direction by the planet. The resulting action 

 upon the motion of the centre of gravity is, therefore, cancelled, so 

 that it must continue to move uniformly iii any direction in which it 

 may have begun to move under any foreign influence to which it 

 may have been subject until 1he mass of the planet will at length 

 come into collision with the edge of the ring and destroy it. Why, 

 then, has not Saturn's ring been long ago destroyed ? It is simply 

 because the disturbing forces have always counteracted their own 

 effects. These disturbing forces are the actions of the satellites, and 

 it is by means of these satellites that the ring is held in its place. 

 They are at once the disturbing and the sustaining agents of the ring, 

 and if there were no satellites there could be no ring. If the satellites 

 were removed, the ring would soon strike against the primary, and be 

 broken to pieces, or resolve itself into satellites. The theory of the 

 action of the satellites in sustaining the ring admits of various forms 

 of illustration. In the first place, each particle of the ring may be 

 regarded as a satellite, which the other satellites disturb in such a way 

 as not to vary, in the least, the mean distances from Saturn, and the 

 disturbance of the eccentricity can only reach certain definite limits, 

 after which it must diminish. Secondly, in consequence of the attrac- 

 tion of the satellites, Saturn describes an orbit about the common cen- 

 tre of gravity of the system ; each particle of the planet tends to 

 move in this same orbit, and also the centre of gravity of the ring tends 

 to describe nearly the same orbit. The orbit would be precisely the 

 same if the attractions of the ring for the satellites were the same as if 

 the mass of the ring were accumulated at its centre of gravity ; but the 

 deviation from this orbit may be safely referred to the laws of periodi- 

 cal perturbations. 



4. It follows from what precedes, that no planet can have a ring, 

 unless it is accompanied with a sufficient number of properly arranged 



