$2 Equipartition of Energy and Radiation Theory. 



we find that, i£ an electron, or (by an extension o£ the 

 argument) a gas molecule, is placed in the radiation field, 

 twice the average energy assumed by a translatory degree of 

 freedom of such an electron or molecule will be 



XJ -» = [^i] v=0 = ^) ( 6 > 



Now, if we decide to measure temperature as a quantity 

 proportional to the average energy of a degree of freedom 

 of a gas molecule, then, in view of (6), this fact alone 

 determines f(T) to be proportional to 1/T ; and if further 

 we choose the size of our temperature degree in the usual 

 way, i. e. in a way which makes U„ = o=RT, we see that 

 a//(T) becomes determined as equal to RT. Thus, again, 

 the origin of the quantity RT is in the radiation formula. 

 This formula determines twice the average energy of a 

 degree of freedom of the molecule to be a/f(T), and because 

 we measure temperature in the way we do, this is equal 

 to RT *, 



According to the usual theories the relation between the 

 gas molecule and the radiation formula is traced through 

 the law expressing the entropy of the system in terms 

 of the probability ; and on this line of argument, the 

 necessity for imagining some form of quantum theory for 

 the radiation appears essential. Developments of the 

 radiation formula not involving this finite quantum concept 

 have been attempted, principally by Larmor ; but though it 

 would appear, from the arguments of Larmor, that the 

 necessity for the finite quantum can really be avoided, 

 there appears to be difficulty in making the theory predict 

 the numerical equality between the constant R in the 

 radiation formula and the gas constant. The view tenta- 

 tively suggested above as to the connexion between the 

 two, is somewhat fruitful in filling in the gap, and it 

 also has a bearing on Poincare's treatment of the problem 

 of radiation, according to which it was claimed as proved 

 that a quantum theory was necessitated by the mere fact of 

 the energy per c. c. of a body being finite and not infinite. 

 It is proposed to discuss these matters in a subsequent 

 communication. 



Department of Terrestrial Magnetism, 

 Carnegie Institution of Washington. 

 August 31, 1916. 



* It must of course be remarked that the above view does not contain 

 as an obvious consequence the Maxwellian law of velocity distribution 

 among the molecules. It would take us too far afield to attempt to 

 inquire into this matter in detail. 



