Origin of the Radiation from Hot Bodies. 223 



collisions as the sum of the amounts of energy radiated when 

 they occur alone. 



If N is the number of free paths which are described in 

 unit volume of the substance in unit time, then, w r hen the 

 collisions are numerous and at random, the energy having 

 frequency between q and q + dq radiated from unit volume in 

 unit time is equal to 



This is not the amount of radiant energy in unit volume at 

 any time, for the energy is absorbed after passing over a very 

 short distance ; we can, however, deduce from it the actual 

 density of radiant energy in the substance as follows : — 



When the system is in the steady state, the energy radiated 

 from unit volume in unit time must equal the energy absorbed 

 by that volume in that time. Let E be the energy in unit 

 volume of the stream of radiant energy of the body when in 

 the steady state, X the electric intensity in the stream, i the 

 current parallel to as; then the energy absorbed per unit 

 volume per unit time is Xz, or, if c is the conductivity of the 

 substance, X 2 c. If K is the specific inductive capacity of 

 the substance measured in electrostatic units, Y the velocity 

 of light in a vacuum, 



4ttV 2; 



hence TT9 



thus the rate of absorption of energy per unit volume is equal 



tO A _T72 



4»\ 



C-TF-E. 



As this in the steady state must be equal to the rate of emission 

 of radiant energy, we have 



c -g— J^=tfg- y <k 2 sm 2 ^- dq. 



When E ? denotes the part of the energy corresponding to 

 waves having a frequency between q and q + dq, we see from 

 (3) that 



When the heat produced by the current represents the 



