RECENT STATISTICAL THEORIES 681 



that in certain reasonings, a freely-flying electron or quantum or even 

 an atom in a region bounded by walls may be replaced by a pattern 

 of stationary waves filling the whole of this region. Thus it seems 

 that the free particle, the oscillator, the stationary wave-pattern, are 

 in close affinity with one another; they may simply represent dififerent 

 ways of looking at the same thing. Though on almost every page 

 of this article I shall write in the language of the strictest corpuscular 

 theory, it is probable that every one of the results could be translated 

 into the language of oscillators or the language of waves. 



There are still assumptions to be made about the individual particles. 

 They are to have position, momentum and energy. Momentum 

 may be separated into mass and velocity; often it is better left as 

 an elementary concept. It will turn out that one of the essential 

 differences between photons on the one hand, electrons and atoms on 

 the other — that is to say, between the particles out of which we shall 

 try to build a picture of radiation, and those of which we shall build 

 models of gases and of electricity in metals — lies in the relation be- 

 tween momentum and energy. 



Experience with matter in bulk leads to the well-known equations 

 connecting kinetic energy K and momentum p with mass m and speed f: 



K = \mv^, p = mv (3) 



and these are supposed to hold for the ultimate particles of matter 

 and of electricity. 



During the years in which the corpuscular theory of light was 

 struggling into existence — for, it will be remembered, light was still 

 considered to be entirely wavelike even after Planck had founded 

 the quantum-theory by his statistics of oscillators — Einstein pro- 

 posed at two different times (1905 and 1917) the following formulae for 

 the energy and the momentum of photons in terms of their wavelength : 



E = hc/\, p = h/\. (4) 



Historically it is interesting that he proposed the latter formula 

 because of certain statistical studies which he had made of the equi- 

 librium between photons and atoms. The verification of the latter 

 by the Compton effect, of the former by the photoelectric effect and 

 many other phenomena, is too familiar to require comment. 



Now from equations (3) we deduce, for particles of matter and of 

 electricity: 



