Energy and Radiation Theory. 81 



the average energy RT/2 per degree of freedom, because this 

 is the quantity which is contained in the appropriate place in 

 the radiation formula. The direct extension of this argument 

 to the case of a gas molecule is not so easy, because we do 

 not know the mechanism by which the molecule is set in 

 motion by the field. Suppose, however, that it is justifiable 

 to extend the result to gas molecules, a step to which we 

 are encouraged by the fact that other considerations lead to 

 equality of the average energy of gas molecules and free 

 electrons ; suppose, in fact, that it is true that in the 

 general case the laws by which the molecules are set in 

 translatory motion are such that 



Twice average energy of gas molecule at temp. T 



A, 4 E A * 

 = Lt -o-g^r , . . (5) 



then, if we take Planck's formula for E x , we have, as 

 before, that the fundamental origin of the quantity R is in 

 the radiation formula and not in the gas molecule, and that 

 it is on account of the occurrence of the quantity RT in the 

 radiation formula that the molecule moves so that the 

 average energy of a translatory degree of freedom is RT/2. 

 A view of this kind is all the more reasonable when we 

 realize that it is only ultimately through the radiation 

 that two gases, for example, which are separated from each 

 other, can come into temperature equilibrium. Even con- 

 duction, when viewed from a fundamental standpoint, 

 probably partakes more nearly of the nature of radiation 

 than of what is ordinarily implied in the term conduction. 



It is of interest to generalize the above arguments in the 

 following form : — 



Suppose that it be known empirically, or by some 

 theoretical argument, that E A is of the form 



-pi _§tt av 



x ~~ \ 4 V^-i' 



where a is a constant, and /(T) is some function of the 

 temperature of which we do not yet know the form. Let 

 us even go so far as to say that we have not yet decided 

 how temperature is to be measured. If we follow the line 

 of the arguments above, and assume the relation 

 U v== o = Lt„ = oX 4 E^/87r, 



* Strictly speaking, the average concerned in (5) is a time average for 

 a single coordinate, while the average concerned in equipartition is an 

 average taken over a number of coordinates at a constant time. The 

 difficulty in this respect is not, however, of fundamental importance, ar.d 

 we shall not dwell further upon it. 



Phil. Mag. S. 6. Vol. 33. No. 193. Jan. 1917. G 



