﻿Theory of Contact Electromotive Force. 265 



every case n is a very large number, so large thai the 

 fractional change in n produced by the communication of an 

 electrostatic charge to a conductor of finite size is negligible 

 in all practical cases. The largeness of n is of course deduced 

 from the results of experiments interpreted by the light of 

 the electron theory. The functions w which measure the 

 work done by an electron in passing from the interior to 

 the exterior of a conductor are also to be regarded as cha- 

 racteristic of each substance. They are functions of the 

 temperature both explictly and implicitly through n. 



Intrinsic Potential Differences. 



We shall begin by considering a vacuous enclosure sur- 

 rounded by insulating walls maintained at a constant tempe- 

 rature 0. We shall also suppose that the thermionic 

 emissivity of the material bounding the enclosure is so small 

 that it may be disregarded. If an initially uncharged 

 metallic conductor is placed inside such an enclosure it will 

 emit negative electrons, the initial rate of emission being- 

 much greater the higher the temperature of the metal. 

 Clearly this process will not go on indefinitely. The positive 

 charge which the metal acquires, in virtue of the emission, 

 tends to pull the electrons back, and ultimately a steady 

 state is reached in which as many return as are emitted in a 

 given time. This steady state will be accompanied by a 

 statistically steady distribution of the external electrons, and 

 also of the external electric potential. The theorem which 

 we have already mentioned enables us at once to write down 

 the relation between the concentration of the electrons n 

 and n at any two external points whose potentials are V 



and V. It is 



e(V-V') 



n w 



where e is the charge on an electron. Since there is equi- 

 librium between the electrons inside and outside the conductor 

 we have turther 



where n and V correspond to any external point, as before, 

 n x is the number of free electrons per cub.centim. inside the 

 metal, V x is the potential at its surface, and u\ is the work 

 done by an electron in crossing the surface of the conductor 

 from the interior. 



Phil. Mag. S. G. Vol. 23. No. 134. Feb. 1912. T 



