4 Prof. Kirchhoff on the Relation between the Radiating and 



angle of polarization, the plane of incidence being a. Let the wall 

 which unites S, and S 2 be so situated that the image cast by plate 

 P of opening 2 lies in it ; and in the place and of the form of this 

 image imagine an opening, which I shall call opening 3. Let 

 opening 2 be closed by a black surface of the same temperature 

 as the rest of the system, and let opening 3 be closed, in the 

 first place by a similar surface (which I shall call surface 3), and 

 secondly, by a perfect concave mirror, having its centre in the 

 image which the plate P casts of opening 1. In both cases the 

 equilibrium of temperature remains undisturbed, and for reasons 

 similar to those mentioned in the last section ; it thence follows 

 that the sum of the intensity of the rays withdrawn from the 

 body by the removal of surface 3, is equal to the sum of the 

 intensities of the rays incident on the body in consequence of the 

 application of the mirror. Let a black screen S 3 , of the tempe- 

 rature of the rest of the system, be so placed that no rays ema- 

 nating from opening 3 can reach the body directly. The first 

 sum is then the intensity of the rays which proceed from sur- 

 face 3, are reflected by plate P, and pass through the opening 1 ; 

 let this be indicated by Q. The second sum consists of two 

 parts : one depending on the body C, which is 



dXer*, 



where r indicates a magnitude depending on the constitution of 

 plate P, and independent of \ ; the second part consisting of 

 rays which have proceeded from some portion of the black wall 

 uniting S! and S 2 , have penetrated plate P, and have been 

 reflected, first by the mirror, and then by P. This portion I 

 shall indicate by R. It is unnecessary further to determine the 

 value of R, it being sufficient to observe that R, like Q, is inde- 

 pendent of the nature of C. Between these magnitudes, then, 

 there subsists the following equation : 



f 



*/\er 2 + R=Q. 



If, now, the body C be replaced by some other black body of the 

 same temperature, e! indicating for this body what e does for the 

 other, then 



{™d>Jr* + R=Q. 



Whence 



i 



d\( e -e , )r* = Q. 

 Now let the index of refraction of plate P be supposed to be 



