CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL 

 LABORATORY, HARVARD UNIVERSITY. 



NOTE ON KIRCHHOFF'S LAW. 



By Griffith C. Evans. 



Presented by George W. Pierce. 



Received May 27, 1910. 



Kirchhoff's Law in its simple statement says that the energy radi- 

 ated at a given temperature divided by the absorption coefficient for 

 that temperature is the same for all bodies of the same shape and size, 

 that is, equal to the energy radiated by a perfectly absorbing body of 

 the same shape and size at that temperature. The relation is easily 

 shown to hold for total radiation, and depends merely on the First and 

 Second Laws of Thermodynamics. But for separate wave lengths, 

 a reduction of the law to a firm thermodynamic basis, though often 

 attempted,^ seems not to have been completely obtained. Unwar- 

 rantable assumptions, sometimes tacit, seem unavoidably to have been 

 introduced. 



The present paper, in order to show the 

 nature of the assumptions that must be in- 

 troduced, attempts to set up a system of 

 assumptions fi'om which the law will rigidly 

 follow. 



Pursuing in the main a method of proof 

 due to E. Pringsheim,2 we take now a body 

 S, in which there is a cavity (see Figure 1). 

 This body need not be all in one piece nor 

 need the cavity be filled homogeneously with 

 one medium. Suppose, however, that there 

 is in the cavity a simple closed surface 2i, 

 enclosing another closed surface 2„ and not 

 touching it at any point. The space between 

 2o and 2i is supposed filled with a medium 



^ For such considerations sec H. Kayser: Handb. derSpcctroscopie, II, 13flf. 



' E. Pringsheim: Einfache Herleitung des Kirchhoffschen Gesetzes, Verb, 

 deutsche Phys. Ges. 3, 81. Also Kayser: Sjjectroscopie, p. 37. 



For a criticism of this proof see M. P. Rudski: Zeitschr. f. Wiss. Photog. 3, 

 217, 1905. A reply by Pringsheim, ibid. p. 281. 



VOL. XLVI. — 7 



Figure 1. 



