between .Radiation and Free Electrons. 15 



hand, a problem which admits of scientific and ordered 

 treatment is the following : to examine at what exact point 

 or points it is necessary to break with the old dynamics in 

 order to obtain Planck's formula for the final partition of 

 radiant energy. 



To begin with, there is nothing incompatible with Planck's 

 formula in the classical laws of propagation of light in free 

 aether. It is well known that the partition of energy is not 

 changed by propagation in free aether — any law of partition 

 persists indefinitely so long as no interaction between aether 

 and matter occurs. Stated analytically, the argument runs 

 as follows : — If F(\, T)d\ is an initial partition of energy, 

 then the final law is F(\, T)dX also, and since this is general 

 enough to include Planck's law, no break need be made with 

 the old dynamics as regards propagation in free aether. 



Next, there is nothing incompatible with Planck's for- 

 mula in the classical laws of thermodynamics as applied to 

 radiant energy. For according to these laws, if F(X, T)dX 

 is the initial partition of energy, the final law, after an in- 

 finite number of thermodynamical processes, can be shown 

 to be of the form cf)(\T)\~ 5 dX (Wien's law), in which </> is a 

 function which cannot be determined by purely thermo- 

 dynamical reasoning. Since this final law is general enough 

 to cover Planck's law, we may conclude that there is nothing 

 in the thermodynamical theory of radiation which is incom- 

 patible with Planck's law. Thus Planck's law in no way 

 compels us to abandon the classical laws of either propagation 

 or of reflexion, compression, &c. of radiation, so long as 

 these latter processes are effected by ideal walls such as are 

 imagined in thermodynamics. The classical laws may stand 

 for free aether and for ideal matter : it is when we come to 

 real matter that the break with the classical laws must be 

 made if w r e are to arrive at Planck's formula. 



In the present paper an attempt is made to carry the 

 investigation further along these lines. The simplest system 

 of real matter which can be imagined is a single electron. 

 I have tried to examine whether there is anything incon- 

 sistent with Planck's law in the classical laws of interaction 

 between radiant energy and a single free electron. To 

 answer this, it is necessary to investigate what would be the 

 final law of partition of radiant energy in a system in which 

 the radiant energy started from any initial law of partition, 

 and had this law modified by encounters with a single free 

 electron, the laws of interaction beino- assumed to be the 

 classical laws. The question is : Will the final law be 

 general enough to include Planck's law? 



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