250 POPULAR LECTURES AND ADDRESSES. 



which we have hitherto supposed ; or let us 

 annul the rigidity of the solid cores of the 

 rings, and give them molecular rotation accord- 

 ing to Helmholtz's theory of vortex motion. 

 For stability the molecular rotation must be 

 such as to give the same velocity at the 

 boundary of the rotational fluid core as that 

 of the irrotationally circulating liquid in contact 

 with it, because, as I have proved, frictional 

 slip between two portions of liquid in contact 

 is inconsistent with stability. There is a further 

 condition, upon which I cannot enter in detail 

 just now, but which may be understood in a 

 general way when I say that it is a condition 

 of either uniform or of increasing molecular 

 rotation from the surface inwards, analogous 

 to the condition that the density of a liquid, 

 resting for example under the influence of 

 gravity, must either be uniform or must be 

 greater below than above for stability of 

 equilibrium. All that I have said in favour of 



March I, 1880 ; and a paper by Hicks, " On the Steady Motion of 

 a Hollow Vortex," read before the Royal Society, June 21, 1883 

 (see Trans. R. S., for 1884). 



