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Proceedings of the Royal Society of Edinburgh. [Sess. 
(H. A. Wilson’s “ thermionic current ”) being found to be a definite function 
of the absolute temperature, which we shall presently employ. H. A. 
Wilson has regarded this emission of electrons as an evaporation of negative 
electricity through the surface of the hot body, determined therefore by 
the nature and temperature of the body and by a definite “ vapour pressure 
of electrons.” Regarded so, the ordinary thermodynamic laws of evapora- 
tion are at once available, and Wilson has shown * that in this way 
Richardson’s expression for the thermionic current may be derived. Now 
it is reasonable to suppose that the emission, though of observable magni- 
tude at high temperatures only, takes place at all temperatures, vary- 
ing in amount only according to the temperature and the pressure of the 
electron “ vapour,” which we may assume to obey the laws for an ideal gas. 
Suppose then that two metals A, B are in contact and that the 
vapour-pressures \ of electrons in the metals are p A , p B , at absolute tem- 
perature 0 . Let us place the arrangement inside a chamber whose walls 
are completely impervious to the electrons and, having completely exhausted 
this chamber, let us fill it with our electron- vapour, at a vapour-pressure p r 
at absolute temperature 6. Lastly, let the whole arrangement be kept at 
constant (absolute) temperature 6 and let the contact potential-difference 
between A and B at this temperature be E. The thermodynamic process 
(assume p<p A <p B )\ is then as follows : — 
Allow a definite quantity of the electron-gas to evaporate out of metal 
A into the surrounding chamber. For convenience this quantity may be 
chosen as that carrying a charge of l'772xl0 7 ^=— ^ electro-magnetic units: 
we have then unit mass of gas to deal with and, in the gas equation 
* H. A. Wilson, Phil. Trans., A, vol. ccii. 243 (1903). 
+ We shall use this term throughout, though more probably, Nernst’s “pressure of 
solution” would convey the conception more clearly. 
f p A >p>p b would be a more convenient assumption, as indicating evaporation out of 
A into the chamber and out of the chamber into B. It has been thought better to avoid 
such a particular case ; in fact any assumption will do. 
