CONTRIBUTIONS TO SCIENCE. 50*7 



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 " capillary force," in the beautiful 

 experiments of M. Plateau. 



In this essay I have shown that such a destructive tendency 

 actually exists, but that by the revolution of the ring it is con- 

 verted into the condition of dynamical stability. 



The investigation of the motion of a ring composed of 

 a continuous liquid, led to the result that the waves set 

 up in the ring would cause it to break up into a number 

 of drops which might revolve as satellites about Saturn; 

 but if the condition of stability was not fulfilled, they would 

 coalesce, forming a smaller number of larger drops, until the 

 condition of stability was secured ; and the same would be 

 the case if the ring were supposed to consist of a number 

 of concentric narrow rings. The 'liquid ring, therefore, did 

 not afford a more satisfactory result than the solid one, 

 though it appeared that the internal friction would produce 

 no sensible effect, and Maxwell had recourse to " the dusky- 

 ring, which is something like the state of the air sup- 

 posing the siege of Sebastopol conducted from a forest of 

 guns 100 miles one way and 30,000 miles the other, and 

 the shot never to stop but go spinning away round a 

 circle radius 170,000 miles." 1 This, however, is not the 

 order in which the investigations appear in the paper 

 before us. 



Having dismissed the assumption of the solid rings, 

 Maxwell investigated the effect of disturbance on a ring of 

 small transverse section, the parts of which are not rigidly 

 connected. The disturbances he treated as made up of 

 " harmonic" elements, according to Fourier's method ; and, 

 first treating the ring as a number of equal satellites revolv- 

 ing round the planet, he found that such a ring " can always 

 be rendered stable by increasing the mass of the central 

 body and the angular velocity of the ring." If the ring con- 

 sist of 100 satellites, the mass of the planet must exceed 



1 See p. 278. 



