98 
PHYSICS: E. H. HALL 
THERMO-ELECTRIC ACTION WITH DUAL CONDUCTION OF 
ELECTRICITY 
By Edwin H. Hall 
Jefferson Physical Laboratory, Harvard University 
Communicated February 16, 1918 
In a paper* presented before the National Academy of Sciences in No- 
vember, 1917, I discussed thermo-electric action in metals on the hypothesis 
of progressive motion by the 'free' electrons only. I have now extended the 
discussion to the case of dual electric conduction; that is, conduction main- 
tained in part by the free electrons (electrons F) and in part by the associ- 
ated electrons (electrons A), the latter passing directly from atomic union to 
atomic union. 
I do this because, though we may not at present have a satisfactory theory 2 
of electric conduction involving such action of the associated electrons, we 
are equally far from having a satisfactory theory of conduction as a function 
of the free electrons only. 
I take it as self-evident that, whereas electric potential-gradient acts upon 
both free and associated electrons, tending to carry them in the direction of 
decreasing negative potential, free-electron pressure-gradient acts on the free 
electrons only. The necessary result of this consideration is the conclusion 
that, if electrons (A) as well as electrons (F) can move progressively through 
a metal, we shall, in a detached bar of metal having a temperature gradient 
from one end to the other, have a constant procession of free electrons from 
the place of high electron-gas pressure, the hot end of the bar, toward the 
place of low pressure, the cold end, while an equal procession of associated 
electrons moves in the opposite direction. For the mechanical tendency of 
the free electrons toward the cold end maintains an excess of negative poten- 
tial at this end, with a corresponding deficiency at the hot end; and the elec- 
tric potential-gradient thus established drives associated electrons from cold 
to hot, while it opposes, without being able entirely to prevent, the movement 
of free electrons from hot to cold. 
The state of mobile electrical equilibrium thus presented to our imagination 
involves no violation of commonly accepted principles. The slight, extremely 
slight, reduction of electron mechanical pressure below the normal equilibrium 
pressure at the hot end of the bar induces there continual passage of the 
electrons from the associated to the free state, evaporation, let us say, with 
absorption of heat. At the cold end, on the other hand, the very slight ex- 
cess of electrical mechanical pressure, above the normal value proper to the 
temperature, induces continual passage of electrons from the free to the asso- 
ciated state, condensation, let us say, with release of heat, The whole opera- 
tion carries heat from the hot to the cold end of the bar, and it is, in fact, 
