740 Prof. 0. W. Richardson on the Electron 



§ 3. The Emission of Electrons. 



It is evident that no sound argument can conflict with 

 Professor Wilson's formula : — 



i + - —wofRe 

 p=A0 * e (U) 



which is quite general, subject to the assumed condition that 

 that the true internal latent heat of evaporation is a linear 

 function of 6. This is clearly shown by equation (51) of my 

 paper. 



The main use of equation (20) is, therefore, that by com- 

 parison with (51) it enables us to deduce a relation between 

 the specific heat of electricity and the temperature variation 

 oh' the latent heat of evaporation. In virtue of the con- 

 siderations brought forward in the last section this should 

 be 



instead of equation (2-1) of the preceding paper. 



There is another point that seems worthy of consideration 

 in this connexion. If N is the number of electrons emitted 

 by a conductor in unit time, n the number in unit volume of 

 the conductor, and w the work they have to do in order to 

 escape, then a calculation based on the kinetic theory shows 

 that 



N = n6>^^y^— / R (16) 



\2irmJ 



On the other hand, we have by thermodynamics 



N = A0i* J ™ 2 ' =K6ie~^eUe^9 d \ . . (17) 



where A. is independent of 0. Equations (16) and (17) are 

 inconsistent unless 



n — constant X 



J R0 



bo 



dO 



1 e -w =Jie w Qo - n) (18) 



Now (16) has only been shown to hold provided the forces 

 to which the electrons are subject are inappreciable except 

 throughout a small proportion of the volume of the conductor. 

 If these or equivalent conditions do not hold,?i and w in (16) 

 do not have a precise meaning without further specification. 



