Quantum of Action. 159 



average energy of an oscillator is kT, and (b) the Kayleigh- 

 Jeans law when equilibrium is established between the 

 oscillators and the aether. These conclusions not being in 

 accord with experimental facts, Planck has recourse to the 

 following main hypothesis. He supposes the oscillators to 

 be uniformly distributed through a finite (not infinitely 

 small) region 



bounded by two of the ellipses mentioned above. The whole 

 of the g, p plane is thus divided into areas each equal to A. 

 These are his regions of " equal probability." It is now 

 seen that the area of any ellipse separating two such regions 

 can be expressed in the form 



j>dg=(n + l)A, 



where n is any positive integer (including zero) and the 

 average energy of the oscillators in the region is 



% t =(n + i)hv. 



The law of distribution is now 



hv nhv 



where / is the fraction of the total number of oscillators 

 situated in the region n. The average energy of all the 

 oscillators is 



E = 7iv 



/ 1 1 \ 



There are, in my opinion, objections to the hypothesis 

 of regions of " equal probability."" It appears to involve 

 energy exchanges of a continuous character side by side 

 with discontinuous exchanges. Indeed, Planck assumes * 

 that his oscillators absorb energy in accordance with 

 ordinary dynamical laws, but emit it in a discontinuous 

 manner. So long as no other way of accounting for the 

 phenomena concerned can be found, such hypotheses may 

 be justifiable ; but no theory can be held to be satisfactory 

 which applies one system of dynamics to the process of 

 absorption and another to that of emission. This, however, 

 is what is done in the theories of Planck and Ishiwara f . 

 Moreover, there is at least one consequence of the con- 

 tinuous absorption hypothesis which is not in good accord 



* M. Planck, Theorie der Warmestrahlung, p. 150, 2nd Edition. 

 + Cf. Jeans, "Report on Eadiation and the Quantum Theory," Phys. 

 Soc. 1914, p. 82. 



