Energy between Matter and Jfither. 95 



suggests that the physical problem is not yet fully threshed 

 out. 



§ 6. Let us assume, as a preliminary to carrying the inves- 

 tigation a stage further, that the transfer of energy from matter 

 to aether does not occur at all on the free-paths of molecules, 

 but that vibrations are set up in the aether at collisions. I£ 

 t is an average time of duration of a collision, the frequency 

 of the waves u forced " in the aether is less than or comparable 

 with t, waves of frequencies much greater than t being, as 

 can readily be shown by analysis which I have already given *, 

 of infinitesimal amplitude. We now see that the ultimate 

 distribution of energy in the spectrum would depend on the 

 temperature from which the material system had started, and 

 the radiation at any instant would depend on the temperature 

 at that instant. A mass of gas might at one time emit a 

 spectrum extending into the ultra-violet ; by the time the gas 

 had cooled to half its former temperature, the spectrum would 

 be a heat-spectrum only. The actual temperature at which 

 the light-spectrum would disappear is easily found, from the 

 analysis already quoted, to be comparable w T ith 1000° C. 



§ 7. Suppose, however, that we now consider a mass of gas 

 shut up in a perfectly reflecting enclosure. The coordinates 

 of the aether must no longer correspond to plane waves in un- 

 limited aether; they must correspond to the principal vibrations 

 of the aether inside the enclosure. The number of these 

 vibrations is still infinite, but the number of which the 

 frequency is below any given limit is finite. Let us suppose 

 that the average time of a collision is t, and that of the 

 infinite series n of principal vibrations in the aether, a finite 

 number s have periods which are less than, or at most 

 comparable with t, the remaining n — s having periods small 

 compared with r. Then, of the n degrees of freedom of the 

 aether, only s receive any perceptible amount of energy from 

 the molecules at collisions. We may say then that the 

 transfer of energy between the material degrees of freedom 

 and s degrees of aether freedom is comparatively rapid, while 

 that to the remaining n — s degrees is very slow. For an 

 enormous time these n — s degrees of freedom will not receive 

 their due share of the energy, while the energy will rapidly 

 equalise itself between the remaining 3N + s degrees of 

 freedom. During this time, the ratio of the energy of the 

 aether to that of the material system is s/3N, and this will 

 generally be very small. 



§ 8. For instance, let us enclose gas at atmospheric pressure 



* ' The Dynamical Theory of Gases,' Chapter IX., or Phil. Mag. 

 August 1903: " On the Vibrations set up in Molecules by Collisions." 



