12 Prof. Kirckhoff on the Relation between the Radiating and 



from various parts of the black covering, have been thence re- 

 flected or refracted through opening 1 towards surface 2, have 

 been reflected by the plate P, and again by the mirror at 3, and, 

 lastly, again reflected by P through opening 1. If M then have 

 the meaning given it in § 10, this last part 



4 



d\Mr*A. 



It may appear doubtful whether the above expressions for the 

 first and third of these portions are correct when C is in such a 

 position that a finite portion of the pencil proceeding from 2 

 through opening 1, and incident on C, is by C reflected back 

 towards 2. Such cases are therefore for the present excluded. 



According to § 10, M = M', and by definition M'=<?(1— A). 

 The third part is therefore 



= r°d\*(l-A)r 2 A, 

 whence we have the equation 



rf\(E-Ae)Ar 2 =0. 



I 



And from considerations identical with those mentioned in § 3 

 with reference to a similar equation, the conclusion may be drawn, 

 that for every value of \ 



E 



A = e; 

 or, putting for e its value as obtained in § 5, 



The proposition we undertook to prove is therefore established, 

 subject to the condition that no finite part of the pencil that 

 proceeds from surface 2 through opening 1, and is incident on 

 the body C, is reflected back by C to surface 2. That the pro- 

 position is true without this limitation, is obvious when we 

 consider that, if the condition in question be not fulfilled, it is 

 only necessary that the body C should be turned through an 

 infinitely small angle in order to satisfy it, and that such a change 

 of position can only cause an infinitely small change in the values 

 of A and E. 



The magnitude indicated by I is, as remarked in § 5, a func- 

 tion of the temperature and the wave-length. The determina- 

 tion of this function is a problem of the highest importance ; 

 and though difficulties stand in the way of our effecting this 

 by experiment, there is nevertheless a well-grounded hope of 



