Absorption of Energy by Electrons. 67 



radiation, the Doppler effect and the change of mass are all 

 allowed for. In the present paper, however, the negative 

 electrons are not supposed to influence each other and the 

 positive charges remain at rest, as in Lorentz's own work. I 

 hope to prove elsewhere that these restrictions can be re- 

 moved without altering the character of the results. Here, 

 too, the radiation is simply assumed as an external field in 

 addition to the other forces. I hope also to show how the 

 radiation may be defined as distinguished from the forces of 

 interaction of the charges, positive or negative, at any in- 

 ternal point of a hot body. 



Let the number dN of electrons having their coordinates 

 ocyz within the volume element dxdydz, and their momenta 

 pqr within the triple element dpdqdr, be given by 



dN" = f(H) dp dq dr dx dy dz (1) 



f(H) is any function of i7, the energy of the electron at 

 that point of the field. Let E K d\ be that part of the com- 

 plete radiation per unit volume for which the wave-length is 

 between X and \ + d\. It is shown in this paper that 



E^--^{logf(H)}®(\)dH=$ir\- i r<f?(\)dIL . (2) 



<I>(\) is a function of X and of H depending upon the 

 nature of the forces. 



R 



f{H) varies as e ne in the distribution required by the 

 kinetic theory, and (2) reduces to 



E x = S7tR6\-\ (3) 



which is Lorentz's result. If, for any cause, f{H) decreases 



JEL 



more rapidly than e'ue, E K has a smaller value than (3) 

 assigns to it. 



The distribution of energy given by (3) is verified only for 

 large values of \6. (3) must therefore be replaced by some 

 such formula as that of Planck : 



E k = ^7rcli\~'°\e^e — l) (4) 



(4) is not deduced from the recognized principles of: 

 dynamics. These, applied to the problem of complete 

 radiation by the general statistical methods of Maxwell and 

 Boltzmann, give us always (3) and nothing else. Lorentz's 

 formula merely expresses the law of equipartition in the 

 form it takes for radiant energy. It involves the same con- 

 sequence : any configuration of a system obeying dvnamical 



F 2 



