and the Partition of Energy in Continuous Media. 249 



express the energy in the form (33), while at the same time 

 treating the system as non-dissipative. If the energy is 

 expressed in the form (33), the quantities (34) do not remain 

 constant, for the energy they represent is subject to dissipa- 

 tion by viscosity. If we wish to treat the system as non- 

 dissipative, we must regard it as an aggregation of molecules, 

 and the energy can no longer be expressed in the form (33). 



24. We come now to the electromagnetic system discussed 

 in § 21. There seems to be no room for doubt that formula 

 (32) accurately represents the partition of energy in the 

 normal state, but the question of whether the system tends 

 to pass into the normal state remains as yet unanswered. 



Light reaches us from stars of which the parallax is too 

 small to measure. The most refined measurements have 

 never yet led us to suppose that its velocity depends either 

 on its intensity or frequenc}^. This and all other available 

 evidence points to the fact that vibrations in free aether are 

 isochronous and free from dissipation, or at least that they 

 may be treated as such in the present investigation*. The 

 energy may accordingly be expressed in the form (33), and 

 the system treated as non-dissipative. It follows at once 

 that the quantities (34) retain their original values — if not 

 for ever, at least for a time incomparably greater than any 

 that could be realized experimentally. It follows that a 

 system consisting solely of free aether could never attain the 

 normal state. 



As soon, however, as matter is introduced into the enclosure, 

 the problem assumes a different aspect. From the necessary 

 interaction between matter and aether, it follows that the 

 energy of the aether can no longer be expressed accurately in 

 the form (33). The energies of the different vibrations into 

 the aether no longer remain constant, for the matter supplies 

 a means of interchange of energy between them. The 

 •question which now becomes cf preponderating importance 

 is that of the rate of transfer of energy. 



25. It is known f that the rate at which energy is trans- 

 ferred to a vibration of frequency p is proportional to a 



* A short calculation will show how safely we may neglect dissipation. 

 Lie-lit reaches us from Arcturus, distant 2x 10 14 miles, and we have no 

 reason to suppose that it is greatly dimmed on its way. However, as 

 we can afford to be liberal in the allowance we make for dissipation, let 

 us suppose that the light, by the time it reaches us, is dimmed to one- 

 billioiith (10 - 12 ) of its original brightness. This means that the light 

 has to travel 70,000 miles (a much greater distance than it could possibly 

 .be made to travel in any terrestrial experiment) before its energy is 

 diminished even by one-millionth of one per cent. 



t ' Dynamical Theory of Gases,' chap. ix. 



