﻿Theory of Long Wave Radiation. 169 



and then we shall have 



s 2 e 2 l m Nu m ivA 



= \/l 



. A' 



66>Vi 





and the expression for the partial energy flux through the 

 element w l thus takes the form 



s/ 



t s~Ne 2 L v ii m ww'AdX 



Sir 6d 2 c 2 r 2 \ 2 ~ ' sVlJ' 



2c0 

 But in virtue of the relation \ = - — this becomes 



A mo . 



We therefore conclude that the emissivity of the plate is 

 given by 



■iVir 



~Ne 2 1 V 

 r 2 k* 





dX 



1 + 



±7r 2 c 2 lJ 

 u, 2 X 2 



2 / 2 ]NV/,„«„,A 

 * - 3V for,;/. , VeVV 



On combining the two expressions for E and A we find 

 that 



1 + ^LfhL 



87T E _ 87T>BU m 2 3 XW 



* (X ' i} - T A 3A^' Y^ 17 ^ 1 ^' 



tlnV 



W 



hich is exactly Lorentz's result if 



u 2 _ ?>u m 2 



ir 



8~~' 



2 37T 2 



w — o" W m ? 



a value which certainly lies within the above limits possible 

 for v 2 , but which can only be said to be satisfied exactly for 



one particular value of I -^ J. 



If, therefore, the formula adopted for a is exact, our 

 analysis verifies that KirchhofFs law does not apply exactly 

 in the case under investigation. Of course the discrepancy 

 is small except perhaps for extremely short waves, but it is 

 worth noticing. 



