298 
PHYSICS: E. H. HALL 
If we take one gram of electrons, each of mass m, we have 
pv = -RT, (3) 
m 
and by substitution in (2) we get 
dp, or (dp) s = --d (j>v). (4) 
2v 
This is the difference of pressure which the free electrons within a metal 
could bear without drift and without the help of electrical force. It may 
be called the static difference of pressure, (dp) s . 
If, now, there exists within a metal a free-electron pressure dp>(dp) s , the 
excess 
dp - (dp) s - or dp-— -d (pv), (5) 
2v 
will be the true mechanical driving force operating to maintain a drift of the 
electrons. Hence the introduction of 'hypothesis (B)' requires the substitu- 
tion of dp — (1 -f- 2v) d(pv) for dp in the second member of equation (4), 
of my paper referred to above, and makes the whole equation read 
(?<-?„)+ [ k i-dP,+ f|<Zi>„ = ± C^(vdp-id(pv)), (6) 
J k Jh k ue Jc k 
where k has the same meaning as the (k a + &/) used in the original equation. 
This is the expression for the Virtual e.m.f.' resident in a detached metal 
bar having one end at and the other at T c . In my previous discussion 
of this matter, not written out in my April paper, I had proceeded as if the 
factor (kf -7T k) could be put with the (pv) so as to give d [(kf -r- k)(pv)]. This 
error led to my giving figure 4 of that paper as the graphical representation, 
on the P-V plane, of the virtual e.m.f. in question. 
The second member of equation (6) can be put into the form 
If 
Ge Jc 
k 
and the graphical representation of this expression is given in figure 1 . Here 
A D is the pv line for one gram of free electrons in the metal; A' D' is ob- 
tained from A D by applying the proper value of the factor (kf -r- k) to each 
value of v; and A' D' is obtained for A D by applying the proper value of 
the factor (k f ^ k) to each value of p. A" D" is obtained from A' D' by 
taking one-half of each value of v, so that the area E A" D" G represents 
-1 ■ vdp of (7). Ai D"i is obtained from A i D x by taking one-half 
pdv of (7). 
