The Vortex Ring Theory of Gases. 23 



1 — n + n. —n. . + . .{r+l) terms 



2 2 3 



(n-l)(n-2)(n-3) . . . . (n-r) 

 V J ' 1.2.3. ...r 



Hence J* cos^Ode j cos (n + 1) 6 + ( - l r cos (n — 2r -f 1 ) 0) J 



-^f-iy M)^- 2 ) ..... (w- r) 

 2^ y 1.2.3 r 



" The Vortex Ring Theory of Gases. On the Law of the 

 Distribution of Energy among the Molecules." By J. J. 

 THOMSON, M.A., F.R.S., Fellow of Trinity College, Caven- 

 dish Professor of Experimental Physics in the University of 

 Cambridge. Received June 4, 1885. 



In any kinetic theory of gases the statistical method of investiga- 

 tion must be used, and since the separate molecules of the gas 

 are supposed to possess some properties to very different extents, it 

 is necessary to know how many molecules there are which have the 

 measure of any given property between certain limits. Thus the 

 question of the distribution of configuration and velocity amongst 

 the molecules is one of the most important problems in any theory of 

 gases. 



This problem has been solved for the ordinary sojid particle theory 

 by Maxwell and Boltzmann, and their researches are the more valu- 

 able as the results do not depend on any assumption about the law of 

 force between the molecules. 



In this paper I shall attempt to solve the same problem for the 

 vortex atom theory of gases. In this case the question is a little 

 more complicated, as the radii of the vortex rings can vary as well as 

 their velocities. This is one of the most striking differences between 

 the two theories ; according to the ordinary theory all the molecules 

 of a gas are of the same size, according to the vortex atom theory the 

 molecules of the same gas vary in size. If this be true, a porous plate 

 of the requisite degree of fineness might play in this theory the 

 part which Maxwell's demons play in the ordinary theory. For let 

 us suppose that we have two chambers, A and B, separated by a 

 porous plate, and that A is filled with gas initially while B is empty, 

 then if the pores in the porous plate are so fine that only the smaller 

 molecules can get through from A to B, then, though some of the 

 molecules will recross the plate, some gas will remain in B, and the 



