EVANS. — NOTE ON KIRCHHOFF's LAW. 103 



surface of K. A surface ^i' is assumed outside Si ; between ^and S^ 

 there is an arbitrary medium. K itself may be solid, liquid or gaseous, 

 though if K is liquid or gaseous the medium in which it is enclosed 

 must be solid. We have then, at the temperature T, 



f f E(\)dSi+ f f [l—A(X)-]e(k)dSi (17) 



J J (.so J J (Si) 



-IL 



e{X) dSi 



(Si) 



since the amount of radiation of wave length A reaching any element 

 of surface dS, from either side is e(\). 

 Hence 



f f E{\)dSi = f f A{X) e{X) dSi, (18) 



J J (Si) J J (Si) 



which is an expression of Kirchhoff' s Law. The expression looks more 

 natural if we denote by A{\) 



f f A(X)e(X)dS, 



I I e(X)dS, 

 J J (SO 

 we then have 



ff E(X)dSi = 1(A) f f e(X)dSi. (19) 



J J (SO J J (SO 



If the ^(A) is a function of the element of surface only, we can by 

 taking a spherical K of the material under investigation deduce from 

 symmetry that 



E{X) = A(X)e(X). 



Discussion of the Assumptions. 



On page 99 certain assumptions are made in regard to the functions 

 S<r,(A) and ^^.^(A), — namely, that as the body 2„ decreases in size, S.rX'^) 

 and 8^XX) approach zero as a limit in such a way that 



A,. = / \S..(X)\dX 

 and 



K,=JjS<rX^)\dX 



both approach zero. This amounts in effect to assuming that 



