Energy between Matter and JEther. 97 



§ 9. We can now trace the course of events when one or 

 more masses of gas are left to themselves in undisturbed aether, 

 At first we may suppose that the total energy is entirely that 

 of the principal degrees of freedom. The transfer of energy 

 between the different degrees of freedom of the gas at any 

 point is, as we know, extremely rapid. The first phenomenon, 

 then, is that the energy of these degrees of freedom arranges 

 itself according to Maxwell's Law. The time required is a 

 small fraction of a second. The next phenomenon, at any rate 

 if the masses of gas are small, is an equalization of temperature 

 by conduction through each mass. Simultaneously with this, 

 however, a transfer of energy is taking place between the 

 principal degrees of freedom of the molecules, and the vibra- 

 tions of low frequency in the aether. This equalises the 

 temperatures of different masses of gas, and endows the aether 

 with a small amount of energy, equal to that of a finite 

 number of molecules of the gas, but small compared with the 

 total material energy. The time required for these phenomena 

 must be measured in minutes, days, or centuries, according to 

 the linear scale of the system. After this, a third transfer of 

 energy begins to show itself, but the time required for this 

 must be measured in millions or billions of years unless the 

 gas is very hot. A transfer takes place between the energy 

 of the principal degrees of freedom of the gas and that of 

 degrees of freedom which may either be in the aether or in the 

 atoms of the gas, but which have the common characteristic 

 that they represent vibrations of high frequency. If the gas 

 is in vacant space, the energy set free streams away into space, 

 but if the whole system is enclosed by an ideal perfectly 

 reflecting boundary, the energy accumulates in the aether. 



Postscript, added June 7th. 



§ 10. As in § 8, the number of degrees of freedom of the 

 aether, of which the frequency is less than k, inside a cube of 

 edge Z, is |Z 3 P/7r 2 V 2 . Hence the number of vibrations of 



frequency between k and k + dk is — 2 ^ 2 k 2 dk. At absolute 



temperature T each degree of freedom possesses energy JRT, 

 where, if the units are those of the C.G.S. system and of the 

 centigrade thermometer, the value of R is 9*3 X 10~ 17 

 {of. "The Dynamical Theory o£ Gases," § 130). Thus the 

 Phil. Mag. S. 6. Vol. 10. No. 55. July 1905. H 



