﻿540 Mr. S. B. McLaren on Emission and Absorption 



II h divided between the two degrees of freedom depends 

 on the am o ant of energy to be divided, that is upon the 

 temperature. 

 March 14, 1911. 



Note added January, 1912. 



It is of coarse true that the equations (95) can now be 

 reduced to Hamilton's by putting 



Pi=l ^dpi, p 2 ' = J e P *dp 2 . 

 The theorem of eqaipartition of kinetic energy gives equal 



average values to p^ '-= — -, •dudp 2 ''^ — r. (See Phi]. Mag. Jan. 



dj)\ dp 2 ' 



1911, p. 48). Here, however, H is no longer a quadratic 

 function of the new momenta and the kinetic energy 

 denned as the sum 



± f dH l f dH 



is not a part of the true energy H. 



Nor does the classical theory of the sether require equi- 

 partition of the radiant energy in the way Rayleighs 

 formula would indicate. That consequence follows only if 

 aBther and matter together form a dynamical system whose 

 laws of motion are deduced from a single formula for the 

 action. Now very much less than this will serve as a 

 mechanical foundation for thermodynamics as Einstein 

 (Annalen der Physik, 1903, xi. pp. 170-187) had already 

 shown. In fact let it be granted that there are : — 



(1) Continuous laws of motion by which the state of the 

 system at any instant can be deduced from its state at any 

 other. 



(2) A unique energy integral of the form 



H = constant, 



H being independent of the time. 



(3) A function p defined by the configuration at time t 

 such that 



It can easily be proved that if there is only one energy H 

 the most general solution p 1 for p is 



Pl = F(H)p ; 

 where p is any solution whatever. Let it be granted that 



