12 PHYSICS: E. H. HALL 
the number of positive ions, atoms lacking each an electron. Within the 
interior of a metal in electrical equilibrium we must have n e = n { . At the 
surface, if the metal has a static charge, we do not have such equality. Now, 
according to my view, the free electrons and the positive ions, which are the 
products of the ionization of the atoms, obey the mass-law, so that everywhere 
in a metal we have 
n e X ni = a, constant. 
If this view is sound, when we take electrons from one plate of a condenser 
and convey them to the other plate, we thereby disturb the electrical equi- 
librium in each metal. If one metal loses, for example, q electrons, we cannot 
have mass-law equilibrium in this metal until sufficient new ionization occurs 
therein to make the total number of free electrons if this metal only J q less, 
and the total number of positive ions \ q more, than at first. In the other 
metal the converse operation must take place, re-association occurring there 
until the number of free electrons is \ q more and the number of positive ions 
\ q less than before. These processes of ionization and of re-association would 
balance each other in heat production if the two plates of the condenser were 
of the same metal, but otherwise they do not. Of course, wherever in the 
metals the ionization and the re-association primarily occur the result will 
presently appear at the surface, since any excess or deficiency of electrons in 
the interior of a metal must correct itself at the expense of the surface. Prac- 
tically, then, we may regard the ionization and the re-association as occurring 
at the surface only. 
Bridgman says that the failure of the equation P = T dv/dT to bear the 
experimental test led Kelvin "to infer the existence of reversible heating ef- 
fects at the surface of a metal when a charge is added to or subtracted from 
the surface, just as he had previously inferred the existence of the Thomson 
heat." Bridgman has thought that this inference was not justified and that 
sufficiently careful experiments would verify the equation. I think, on the con- 
trary, that Kelvin's inference was sound, that the ionization and re-associa- 
tion phenomena which I have indicated are precisely the reversible heating 
effects at the surface which he infers, but does not visualize, and that the 
equation in question will never be justified by experiment. 
The other line of argument begins with a metal in equilibrium with a sur- 
rounding electron atmosphere contained within an enclosure otherwise vacuous. 
The following quotations are from the second chapter of Richardson's Emis- 
sion of Electricity From Hot Bodies: 
"In this steady state there will be a definite number n [of electrons] per 
unit volume, on the average, in the vacuous enclosure, and they will exert a 
definite pressure p. If the enclosure is provided with a cylindrical extension 
in which an insulating piston can move backwards and forwards, this pressure p 
can be made do work against an external force." "The relation between the 
pressure of these electrons and the temperature of the enclosure can be found 
