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XI. On the Partition of Energy behceen Matter and 



Mther. By J. H. Jeans, M.A., Fellow of Trinity 



College * 

 § 1. rrHE question discussed in the present paper is one 

 JL which I stated in an earlier paper on the Theory 

 o£ Gases (Phil. Trans, cxcvi. p. 397, 1901) as follows:— 



" If an interaction between matter and aether exists, no 

 matter how small this interaction may be, the complete 

 dynamical system will consist of the molecules of the gas, 

 together with the aether, and must therefore be regarded as 

 a system possessing an infinite number of degrees of freedom. 

 Applying Boltzmann's Theorem to this system, we are merely 

 led to the conclusion that no steady state is possible until all 

 the energy of the gas has been dissipated by radiation into 

 the aether. This application of the theorem may or may not 

 be legitimate, but it is, I think, certain that no other 

 application is legitimate." 



The same question has recently been discussed by Lord 

 Rayleigh in ' Nature '*. In the present paper, I have tried to 

 investigate the legitimacy of applying the theorem of 

 equipartition to a system consisting of both matter and 

 aether, assuming for the present that this matter is in the 

 gaseous state. 



Let us, to take the simplest case first, consider a gas of 

 which the molecules are rigid spheres or point centres of 

 force, possessing no internal degrees of freedom, and acting 

 on one another partly through " material" forces and partly 

 through their interaction with the aether, this action beino- 

 very small except when two molecules are near together. If 

 there are N molecules (A, B, 0, . . .), we can suppose the 

 configuration of the system to be specified at any instant by 



(i.) 6N coordinates x a , y a , z a , u a , v a , w a , oc b , y b , . . . . giving 

 the positions and velocities of the molecules, and 



(ii.) m coordinates f x , % 2 , f*» (<?• g- components of 



electric and magnetic force) giving the state of the 

 aether at every point, these coordinates being- 

 independent. We here suppose that any relations 

 which must be satisfied in the free aether (e. g., the 

 vanishing of the divergence of the electric and 

 magnetic forces) have already been taken into 

 account. 



* Communicated by the Author. *. 



t April 13th and May 16th, 1905. The present paper was written in 

 March, and was sent to the Phil. Mag - , immediately after the appearance 

 of Lord Kayleigh's first letter. It is therefore not intended as a reply 

 to the second letter, although the questions discussed happen to be much 

 the same. The postscript was, however, written with special reference to 

 the letter of May 16th. 



