122 B. Galitzine on Radiant Energy. 



with respect to (£). If we start with the general equations of 

 the electromagnetic field the electric force F n at a point, 

 which corresponds to any given time of swing, must be a 

 periodic function of the time. Let the corresponding ampli- 

 tude be a n . If the force were constant we should have for 

 the energy contained in unit volume 



» = ^ F2 > (W) 



k being the dielectric constant of the external medium. 



But in our case F is variable. To every ¥ n there corre- 

 sponds a particular dielectric constant k n , but the energy in 

 unit volume for these particular swings is clearly proportional 

 to a 2 n . Since k may be put equal to unity for all swings in 

 vacuo, the total energy per unit volume (e) is obtained as a 

 sum of the followino- form, 



e = const. 2 aj[, 



the summation being extended to all vibrations which the 

 body is capable of emitting at the temperature T. 



a\ is a function of T and n. 



«1=/(T,») (20) 



The function / depends directly on the distribution of 

 energy in the normal spectrum, the term " spectrum " in- 

 cluding all possible rates of vibration. 



If the energy is distributed in a continuous manner 

 throughout the spectrum, the above summation becomes an 

 integral. 



Let <f>(n)dn denote the probability of occurrence of waves 

 whose rate of vibration lies between n and n + dn, then 



« W =»(T) 



e = const. f/(w, T)$(n)dn (21) 



For a perfectly black body which exercises no selective 

 absorption, <f>(n) is constant, but we may leave equation (21) 

 in its more general form. From (15), (1), and (3) it follows 

 that 



T 4 = const. f" (1 /(n, T)cj)(n)dn (22) 



The expression under the integral sign is a quantity which 

 is proportional to the square of the corresponding electrical 

 displacement. 



We thus obtain the following result. The absolute tern- 



