EVANS. 



NOTE ON KIRCHHOFFS LAW. 



101 



The principal difficulty of the proof lies precisely in this step. The 

 purpose is to make as modest a requirement as possible for the func- 

 tion A (A.). We shall assume that there exist, or can be constructed, 

 physical bodies such that the resulting assemblage of absorption coeffi- 

 cients is what we may call densely distributed between some two 

 absorption coefficients that are distinct for every value of X. We 

 define densely distributed as follows : 



Let A' (A) and A" (A) be two functions positive or zero and contin- 

 uous for all positive values of A. Let /(A) be any function finite and 

 continuous for all positive values of A, such that 



or 



^'(A)>/(A)>^"(A), A>0, 

 ^'(A)^/(A)<.r(A), A>0, 



Figure 2, 



and let 8 be any quantity > 0. We say then that the functions A (A) 

 are densely distributed between A' (A) and A" (A) provided that no 

 matter what /(A) and 8 are taken, there is an A (A) such that 



|/(a)-^(a; 1^8, 0<A. 



We shall assume that -4i(A) and Ai(X) are independently densely 

 distributed between two functions ^i'(A) and^i"(A), and two func- 

 tions -4 2' (A) and A^" (X.) respectively, where 



^/'(A) >^/(A), 0<A, 

 and ^/'(A) >^2'(A), < A. 



Suppose now that ei (A) 4: ^i (A) at some value 



A = Aq, < Aq. 



