132 PROCEEDINGS OF THE AMERICAN ACADEMY. 



It might be supposed that we could remedy this defect by assuming 

 the existence of two classes of oscillators, the first obeying the classical 

 laws and the second obeying Planck's assumptions, and in that way 

 account for both optical and thermal phenomena. This hypothesis, 

 however, does not seem tenable. 



For although the classical oscillators would do their best to account 

 for other light phenomena, they would tend to give Rayleigh and 

 Jeans's radiation law (which any system obeying the classical dyna- 

 mics must give) rather than Planck's. Or, in terms of Planck's deri- 

 vation, their entropy, computed from the thermodynamic probability, 

 would be different from that of his Oscillators because their distribu- 

 tion on the energy diagram would be different. Hence the radiation 

 law would be different also, if any noticeable percentage of these 

 oscillators were present. Moreover, Jeans's law, which they would 

 tend to make the radiation obey, gives an intensity whose ratio to 

 Planck's becomes infinite rapidly as XT diminishes. Thus an ex- 

 tremely small percentage of classical oscillators would give large devi- 

 ations from Planck's law, while the Planck oscillators would not give 

 the well known relations between absorption and dispersion, and 

 other optical laws that are explained by the classical theory. 



Moreover, unless the percentage of each class of oscillators for each 

 frequency were exactly the same for every substance at each tempera- 

 ture the distribution of energy in the spectrum of a cavity would 

 depend on the substances contained in its walls. Such a result is well 

 known to be contrary to the second law of thermodynamics. 



As Planck 2 says, the assumptions he makes are not the only ones 

 that can lead to his law of radiation. The object of the present 

 investigation is therefore to see whether the abandonment of the 

 classical electrodynamics and its explanations of these and other 

 phenomena is really necessary, and if it is not so, to find a mechanism 

 giving both heat radiation and optical phenomena, and at the same 

 time consistent with other phenomena as far as possible. The con- 

 clusion is that it is not necessary, and that the formula can equally 

 well be derived from other assumptions, inconsistent with the classical 

 mechanics only as applied to the internal structure of the electron, 

 and consistent with the classical electrodynamics and its explanations 

 of many phenomena; and, moreover, this explanation is based on a 

 mechanism which has been shown by Parson 3 to be very useful in 



2 "Heat Radiation," English translation by Masius, 154 (1914). 



3 Not yet published. 



