PHYSICS: E. H. HALL 
101 
tial-difJerence between the two ends of the bar. The quantity expressed by 
the whole first member I shall call the virtual e.m.f., resident in t,he bar be- 
cause of its temperature gradient. 
The form of the second member shows that the virtual e.m.f. can be repre- 
sented by an area on the P-V plane. Thus, if the line A D in figure 2 rep- 
resents the pressure-volume relations of the free electrons for the whole 
length of the bar, so that 
c h 
area EADG = I vdp, 
we shall have 
area EA'D'G = I Kf .vdp, 
k a + kj 
FIG. 2 
provided we make the width of this area correspond at every height to the 
value of kf/ (k a + kf) for that height. 
Without the conception of dual conductivity and specific attraction we 
should, as my previous paper 1 shows, have in place of (4) the simple equation 
GeX^ 
with dual conductivity but without specific attraction we should have 
th 
k a + k 
vdp. 
Obviously, then, the participation of the electrons (A) in the conductivity 
reduces the e.m.f. due to the temperature gradient in the bar. In fact, the 
part which associated electrons play in thermo-electric action is analogous to 
that played by entrained water in the work done by steam. The larger the 
