Origin of the Radiation from Hot Bodies. 225 



which energy is absorbed is cX 2 , and ^X 2 is the mean value 

 of X 2 . Comparing these expressions, 



N^ 2 2 

 m (f 



Substituting this value in equation (9) we find 



„ 1 mK . 9 9 7 



If we take the form given by equation (5) for <£ x we have 

 Bj-/!^-*£W .... (10) 

 while if we take (7) we have 



^=l'^*-^<f<k (ii) 



In each o£ these expressions a represents the time of a 

 collision. When the waves are so long that qa is small, these 

 two expressions are identical and agree with that given by 

 Lorentz, provided we assume that the kinetic energy of the 

 corpuscle is the same as that of a molecule of a gas at the 

 temperature of the radiating body, i. e. is equal to oc6 if is 

 the absolute temperature and a =1*42 x 10 ~ 16 . 



On this assumption (11) becomes 



If, as is usual, the radiation is expressed as a function of 



2ttV 



the wave-length X, then since q = — r— , E , the rate at which 



radiant energy with a wave-length between X and \-j-d\ 

 passes through unit area is given by the equation 



E A =-^--T- r e k a d\ (12) 



We know from the researches of Wien and others that if 

 the Second Law of Thermodynamics holds for radiant energy 

 E A must be of the form 



where <f>(X$) is a function of \0 and the same for all bodies. 



