﻿= % = \/l ( 13 > 



930 On the Deduction of Wieh's Displacement Law. 



for some other temperature, 6 2 > The abscissa \ x of any point 

 on the original energy-curve is changed to a new value X 2 , 

 such that 



h 



Ait ,-vke same time the ordinate of the point changes so that 



and the area under the curve, which represents the integral 

 density /?, changes so that 



^ = ~. (15) 



But w-e know by the Stefan-Boltzmann law * that for .diffuse 

 black radiation at B 1 and 2 



Pi 

 Pi 

 w T hence it follows that 



(IT M> 



*-i < 17 > 



From equations (13) and (17) we thus obtain the relation 



Mx = ^2^, (18) 



and the displacement law contained in equations (12) and 

 (18) may be stated as follows : — Given the spectral energy 

 curve of black radiation at any temperature l9 to construct 

 the curve for any other temperature # 2 , multiply the abscissa 



of each point by ~ and the ordinate by l^\ . "Corre- 

 sponding 5 ' points on the two curves have the same value 

 of \d. 



From this we may easily deduce the more familiar special 

 forms of the displacement law 



\»«.0 = const, 



max. 



P™»^ KL T = const., 



rmax. max. ' 



5 



and p max = const, x 5 , 



# The deduction of this law from the value of the radiation pressure 

 p = p/3, by using the principle of section 8, is so simple that it may be 

 omitted here. 



