80 Dr. W. F. Gh Swann on Equipartition of 



where no other significance is attached to h and k other than 

 that they are constants, k is at present in no way associated 

 with a gas molecule, and, indeed, we shall not attach any 

 significance to T other than that it represents the quantity 

 which we measure as the temperature. Let us in fact for 

 the moment look upon (4) as a mere empirical relation. 

 Let us now suppose as a very special case that there are 

 some perfectly free electrons in the radiation field . Although 

 we may not know the equations of motion exactly, yet we 

 know them with a sufficient degree of approximation to be 

 able to ascertain with some accuracy how the electron will 

 behave in the field. Planck has shown that an oscillator of 

 frequency v, when placed in a radiation field, will take up an 

 average energy U where Ex = 87rU/\ 4 . Hence, twice the j 

 average value of the kinetic energy assumed by a resonator 

 of frequency v, when placed in a radiation field, will be 



tt X " ^ hv 



e kT -l 

 For v'^sQ we obtain the case of a free electron, and * 



U v=0 = Lt v=0 -Q — = &T. 



07T 



Thus, quite apart from any theory as to the origin of the- 

 formula (4) and as to the meaning of k and T, if only we know 

 that (4) is correct, we can say that twice the average energy 

 per degree of freedom of an electron placed in the field will 

 be kT. We have, in discussing this maiter, so far used kT 

 instead of RT in order to enforce the idea that we are not 

 looking upon the kT occurring in (4) as fundamentally equal to 

 twice the energy of a degree of freedom of a gas molecule, 

 but for the sake of uniformity we may now replace k by R, 

 and we may then note that on the above view we are not 

 adopting the attitude that the quantity RT occurs in the 

 radiation formula because RT/2 is the average energy of one 

 component of the motion of the free electron in the field, but 

 rather are we adopting the view that the electron moves with 



* This step is not quite rigorous, for although it appears generally to 

 be assumed (see Jeans, " .Report on Radiation and the Quantum Theory," 

 p. 14) that a free electron may be treated as an oscillator of zero 

 frequency, the nature of the mathematical reasoning does not appear to 

 warrant this assumption rigorously. It is proposed to enter into this 

 matter more fully in a later communication ; but as the practical con- 

 clusions are not materially affected, it is not intended at present to> 

 complicate the considerations by going more deeply into this matter. 



