PHYSICS: E. H. HALL 
99 
somewhat analogous to the action of a steam heating- system, the free-electron 
movement corresponding to the stream of steam and the associated electrons 
movement to the return flow of the water. 
My conception of the action, for a case in which there is no lateral loss or 
gain of heat, is set forth diagrammatically in figure 1, in which the dotted 
lines indicate movement of the free electrons and the full lines movement of 
the associated electrons. 3 
In my previous paper, 1 dealing with the hypothesis of progressive motion of 
'free' electrons only, I rejected as unnecessary the assumption of a specific 
attraction of metals for electrons. But with the more complicated condi- 
tions dealt with in the present paper we cannot avoid this assumption; for 
without it we should have thermal conduction without initial difference of 
temperature, and so a violation of the second law of thermodynamics, in a 
bar of alloy varying in composition from metal a at one end to metal /3 at the 
other. There must be no progressive movement of free electrons from one 
end to the other, or of associated electrons in the opposite direction, in such 
a bar. The superior mechanical pressure of the free electrons at the a end 
will produce a slight initial movement establishing a potential gradient along 
C 
FIG. 1 
the bar, the a end becoming positive and the /3 end negative; but the influ- 
ence of this potential gradient on the associated electrons must be offset by 
a specific atomic attraction directed toward the /5 end. It is reasonable to 
suppose that the smaller free-electron density at the /5 end is due to the 
superior attraction of the (3 positive nucleus compared with the a nucleus. 
The resulting equilibrium, the inhibition of circulation of the electrons from 
one end to the other of the bar and back, is analogous to the equilibrium in 
a system made up of water, water-vapor, and a solution-column sustained by 
osmotic pressure. The upper end of such a column, with its reduced vapor- 
pressure, corresponds to the (3 end of our bar with its small free-electron 
pressure. The force of gravitation, directed from the top to the bottom of the 
column, is analogous to the electrical potential gradient from the (3 end toward 
the a end of the bar. 
Naturally the question arises whether a bar of one metal having a tem- 
perature gradient, and a free electron density rising with the temperature, 
has not a differential specific attraction tending to move electrons toward 
the cold end. There may be such an attraction, and it will be well for us to 
take account of it, but where there is a temperature-gradient we are not 
