68 Mr. S. B. McLaren on the Emission and 



laws, and any distribution of its motion, must be regarded 

 as equally probable with any other in which the total energy 

 is the same. Planck begins with the counter assertion that 

 all distributions are not equally likely, and deduces (4) by 

 reasoning in which ordinary dynamics is ignored. 



The kinetic theory is statistical, and statistics do not 

 necessarily throw any light on an individual case. In our 

 actual world, energy is not, in fact, distributed as (3) would 

 suggest. It may perhaps be maintained that though 

 dynamical laws do not require (4), yet they may permit 

 the distribution it represents. Hence the importance of 

 Lorentz's method. He deals with a process of radiation 

 and absorption almost certainly at work in metals — a process 

 which does actually bring about for long waves the distribu- 

 tion of energy his formula requires. In metals there are free 

 electrons, and Richardson's experiments even indicate that 

 as between them the distribution of energy is approximately 

 at least that required by the kinetic theory. I have here 

 shown that, in so far as these electrons obey the laws of 

 dynamics and are distributed in the manner required by the 

 kinetic theory, they must produce equipartition of the radiant 

 energy. &h_ 



It has often been suggested that the factor <? EA0 in (4) 

 may arise somewhat thus. Radiation requires a force acting 

 upon the electron during its collisions with the positive 

 charges. In such a collision the force and the acceleration 

 will reach a maximum and decrease again. For a simple 

 example, take them proportional to (c^ + t 2 )' 1 , where t is the 



2rr 

 time. The radiation of period — varies as 



P 



I ev^ + t^dtx] e-^X^ + t^dt, 



<J — 00 ,J — 00 



and this, it can easily be proved, contains the factor e~ 2 P a . 



We need only choose such a law of force as will make a a 

 multiple of O' 1 , and we have the factor required for such 

 formulae as (4). The result of this paper shows, however, 

 that the absorption also contains this factor e~ 2 P a , and that 

 it disappears from the expression for the complete radiation, 

 depending as that does only upon the ratio of emission to 

 absorption. Whoever wishes to avoid the conclusion must, 

 it seems to me, resign the whole system of dynamics from 

 which it is here deduced. 



