10 Prof. Kirchhoff on the Relation between the Radiating and 



k 

 Applying this proposition, and representing by 7 the ratio -, 



in whichever direction the ray passes between the points x l y l 

 and x q y v an expression is obtained for K and K' which only 

 differs from that above obtained by the occurrence of 7 as a 

 factor under the integral sign. 



The equality of K and K' therefore still subsists, even when 7 

 has different values in the rays into which any one of the com- 

 pared pencils may be considered as divided ; it is, for example, 

 unaffected if any part of the pencil be intercepted by a screen. 



§ 9. The following proposition may also be proved of the 

 same pencils as were compared in the last section. Of the 

 pencil which proceeds from 1 to 2, consider at 2 that part which 

 consists of waves whose length lies between \ and XdX, and let 

 it be divided into two components polarized in « 2 and b T Let 

 the intensity of the first of these components be E.d\. Of the 

 pencil that proceeds from 2 to 1, consider at 2 the part consist- 

 ing of waves whose length lies between \ and \ + d\, and divide 

 this into two parts polarized in a 2 and £ 2 . Let the intensity of 

 that portion of the first part which arrives at 1 be R'd\. Then 

 must 



H = H'. 



The proof of this proposition is as follows : — Let K and K/ 

 have the same meaning as in the previous section, L and L' 

 being the magnitudes that K and K' become when planes a } and 

 £, are interchanged. Then L=L', just as K=K', and also 



H = K + L; 



for rays polarized perpendicularly to each other, provided they 

 are parts of a non-polarized ray, do not interfere when they are 

 brought back to a common plane of polarization ; and, according 

 to § 4, surface 1 emits none but non-polarized rays. 

 Lastly, we must have 



H'=K' + L', 



because two rays, whose planes of polarization are perpendicular, 

 do not interfere. From these equations it follows that H = H 7 . 



§ 10. Let fig. 2 have the same meaning as in § 3 ; only let the 

 body C be no longer black, but a body of any kind. Let open- 

 ing 2 be closed by surface 2 ; then a pencil proceeding from this 

 surface through opening 1 reaches C, and is there partly absorbed 

 and partly dispersed in various directions by reflexion and refrac- 

 tion. Of this pencil between 1 and 2 let that part be considered 



no change of refrangibility such as occurs in fluorescence ; this limitation, 

 however, ceases to be necessary if, in the application of the proposition, 

 only rays of a given length of wave are regarded. 



