﻿Partition of Energy and Newtonian Mechanics. 383 



metal ma)* be less, but is certainly not greater, than that 

 of hydrogen (11 volts). But on this view no explanation, 

 consistent with the measurements, can be offered o£ the 

 difference between the various states B'. It appears certain 

 that these differences cannot be due to the presence of the 

 Ci double-layers," the existence o£ which has been proved by 

 Seeliger ; if such double-layers were formed at all in the 

 conditions of thesa experiments, it seems that the ionization 

 must take place at the outer surface of them. 



Leeds, December, 1913. 



XLI. On the Law of Partition of Energy and Newtonian 

 Mechanics. By G. H. Livens *. 



VARIOUS attempts have been made, notably by Jeans f 

 and Lorentz J, to prove that the only possible law of 

 steady thermal radiation deducible from ordinary Newtonian 

 mechanical principles is that which corresponds to equi- 

 partition of energy among the various oscillations, a law 

 w T hich is, however, totally in disagreement with the actual 

 state of affairs as experimentally determined §. Ultimately 

 these proofs reduce to the fact that equi-partition of energy 

 among the various large number of coordinates of any 

 dynamical system represents the only possible average par- 

 tition which can reasonably be expected in any steady 

 state. 



It is therefore concluded that the PJanck formula of radia- 

 tion necessitated by experience is inconsistent with our 

 ordinary mechanical principlesy and therefore necessitates 

 an essential modification in our usual stock of dynamical 

 notions. Jeans even goes so far as to prove that the only 



* Communicated by the Author. 



t Phil. Mag. Dec. 1910. 



% Vide A. Eucken, 'Die Theorie der Strahlung und der Quanta' 

 (Halle, 1914). 



§ It is to be insisted that, although the equi-partition law apparently 

 provides the right formula for long wave radiation, its application even 

 in this part of the spectrum is open to certain objections. In pure 

 thermal radiation, which presumably furnishes a continuous spectrum 

 which would defy all attempts at resolution, the total number of dif- 

 ferent wave-lengths in any small range of extent dX even at the long 

 wave-length end of the spectrum, is infinite, or at least must be assumed 

 to be so in order to secure continuity of the spectrum. There would 

 therefore be an infinite number of different oscillations which on the 

 average secure the same finite amount of energy according to the equi- 

 partition law. There would, therefore, be an infinite amount of energy 

 associated with the small range dX in any part of the spectrum. 



