98 PROCEEDINGS OF THE AMERICAN ACADEMY. 



that is fixed rigidly with 2i wherever in the cavity 2i may be. 2o is 

 fixed rigidly in this medium. We shall regard Iq as a slab whose dimen- 

 sions are small in regard to the other dimensions of the cavity, and 

 whose thickness is small in comparison to its width and height. This 

 surface Sq we consider filled with various substances ; we may have it 

 so that the two faces consist of different materials. Let us denote 

 the two surfaces by a-i and o-g, each of area a-. 



We have two quantities of energy to consider in regard to So, that 

 which passes out of 2o, and that that passes in. The amounts of en- 

 ergy that in unit time pass out of 2o at wave lengths between \ = a 

 and X = b through the two faces o-i and 0-2 we can denote respectively 

 by 



<r£K, W d\ + HnJ^ (1) 



and 



crfX iX)d\ + H^.T (2) 



where E^ (X) and E^J^X) are functions of the substance of the element 

 of surface, of its temperature, and of the nature of the medium in which 

 it is immersed, but not of the temperature or position of other bodies 



in its neighborhood, i/21 and H12 are two functions that depend 



on the surrounding conditions and approach zero as 2o is removed fi-om 

 the influence of other radiating bodies ; they represent the amounts of 

 energy at wave lengths between X = « and A = b, transmitted through 

 2o from 0-2 to o-i and from o-i to <ti respectively. We shall denote the 

 total amounts of energy transmitted by Hzx and Hi2- These assump- 

 tions that we have made in regard to E^^ (A.) and E^^ (A.) constitute 

 essentially Prevost's Law of Exchange. 



The amounts of energy at wave lengths between k^ a and \ = b 

 that in unit time reach Sq at the two faces o-i and o-^ from outside, we 

 can denote respectively by 



'fXw 



d\ (3) 



and 



(4) 



rJV_(X)A 



and the total amounts of energy that in unit time enter 2o through the 

 two faces o-i and o-j respectively by 



