﻿Deduction of Wien's Displacement Lata. 927 



whence upon developing, rearranging, and dividing by p\d\v 



we have 



4 Av &d\ Aft 

 3 v dX p, 



0. 



But since dX changes in the same ratio as X, 



AdX_ AX^ 

 (iX X 



and if we eliminate v by equation (9) we have 



5 AX + ^ =0? . . . . 



* Px 



or 



p^\ 5 = const 



The meaning of this result is that if approximately mono- 

 chromatic diffuse radiation of strength R^X and density 

 p\d\ is compressed or expanded adiabatically and infinitely 

 slowly, the quantity p k changes as the inverse 5th power of 

 the wave-length, X itself being subject to equation (10). If 

 the strip A (fig. 1), of width d\ and height p\, represents 



(11) 



(12) 



i\ 





X 



the original energy density, the strip B, which represents the 

 energy densitv after compression, has its height increased in 

 the ratio of the 5 th power of the ratio of decrease of the 

 width or of mean wave-length. Its area is therefore pro- 

 portional to the inverse 4th power of the wave-length. 



This change of density and the accompanying change of 

 R x dX do not interfere with the validity of the reasoning by 

 which we found the value of n in equation (4). For since 

 the motion is infinitely slow, the values of X\\d\ which have 

 been cancelled from the numerator and denominator may be 



