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XX. A Note on Radiation. By R. H. Kent, Instructor, 

 Department of Electrical Engineering, University of Penn- 

 sylvania*. 



ATTENTION should be drawn to a fundamental fallacy 

 in the deduction of KirchhofPs law for radiation. To 

 deduce it, it is necessary to establish the proposition that 

 there is no net transfer of energy by radiation across the 

 boundary of two abutting media when they are at the same 

 temperature, or that the radiant energy transmitted across 

 the boundary in unit time in one direction is equal to the 

 amount transmitted in the opposite direction. The reasoning 

 by which this proposition is established is as follows : — 



From the equality of temperature of the two media it is 

 correctly inferred that there is no total net transfer of energy 

 across the boundary. It is next assumed that transfers of 

 energy due to temperature differences are accomplished in 

 two ways, by radiation and by conduction, and, moreover, it 

 is tacitly assumed that the process of conduction involves no 

 energy transfer by radiation. Then, since there is no tem- 

 perature gradient, it is correctly inferred that there is no net 

 transfer by conduction, and hence (in view of the fact that 

 the total net transfer is zero) that there is no net transfer by 

 radiation, which is the proposition to be established. 



The fallacy referred to consists in the tacit assumption 

 that the process of conduction involves no energy transfer 

 by radiation. Now conduction in the sense used in the 

 deduction of KirchhofFs law is a net energy transfer, the 

 rate of which is proportional to the vector temperature 

 gradient. Such an energy transfer may conceivably, and in 

 all probability does, involve a transfer of energy by radiation 

 from molecule to molecule of the conducting substance, 

 which in certain cases may fail to vanish with the tem- 

 perature gradient. In general, for example in the interior 

 of a homogeneous isotropic body, it is likely that the 

 radiation part of the energy transfer involved in conduction 

 vanishes with the temperature gradient, but across the 

 boundary between two different media it is easily conceivable 

 that this is not the case. That is to say, it is not unlikely 

 that across the boundary between two media at the same 

 temperature there should flow an energy current in one 

 direction conveyed by impacts and in the opposite direction 

 an equal energy current of radiation. 



* Communicated by the Author. 



