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XXXIX.— ON CUEEENTS OF GAS IN THE VOETEX ATOM 

 THEOEY OF OASES. By GEOEGE FEANCIS 

 FITZGEEALD, A.M., F.T.C.D. 



[Read, June 5, 1884.] 



Mr. J. J. Thomson, in his book on Yortex Atoms, has called parti- 

 cular attention to the fact that the momentum of a vortex ring being 

 proportional to its area, and its velocity through the medium get- 

 ting less the greater its momentum, the velocity of hot simple vortex 

 atoms is less than that of cold ones. Professor Osborne Eeynolds, 

 in his review in Nature, December 27th, 1883, of Mr. J. J. Thom- 

 son's book, called attention to the discrepancy that exists between 

 this result and the fact that the velocity of sound is greater in hot 

 than in cold gas. Now, on considering how the velocity of sound in 

 a gas composed of vortex rings would be propagated, it is at once 

 evident that the usual equations of motion do not apply to a system 

 of atoms whose momentum is not proportional to their velocity, 

 and this at once raises the question. What is the momentum of a 

 current of vortex atoms ? The answer to this of course depends on 

 what the nature of a current of gas formed of vortex atoms is sup- 

 posed to be. If it be supposed to be a current of the medium car- 

 rying the vortices with it, and if it be further supposed that the 

 amount of medium carrying a given mass of vortices is independent 

 of their size, then the momentum of the current will be, as we 

 know it is, independent of the temperature of the gas. These 

 assumptions, however, seem quite at variance with Mr. J. J. Thom- 

 son's investigation as to the relative velocity of hot and cold vortex 

 atoms, where he assumes that each vortex atom moves, independently 

 of the rest, through a medium at rest, and carries its momentum 

 with it, and that the general effect is simply the superposition of 

 the effects due to these independent vortices. The assumption as 

 to the nature of a current of gas, that is consistent with this method 

 of treating the subject, is the usual assumption that a current of gas 

 consists in the motions of the molecules being so polarized that 

 there are a greater number of molecules moving in the direction of 

 the current at any one time than in any other direction, hut that 



