16 DIFFERENCE
IN
POTENTIALS
where
the
second
index denotes the coordinate of the electrode.
We
obtain,
hence,
the
equation
W
n.E.(H2-^)
=
"W
V
"
*
If the electric potentials
in
the
cross
sections
of
the electrodes
inside the solution
are
denoted
by
i1
and
i2,
integration of
the first
equation
(1)
yields
-
n.E(w,
Ti
n [P
-
P
]
+ n RTlog
H.2.
ml
m2
/»!J
m
0
Vu
where
v1
and
v2
refer
again to
the
cross
sections
of
the electrodes.
Adding
these
equations,
one
obtains
(3)
(n2~ t2}
(Hj-tj)
=
(m)2
-
(An)t
n
RT
n v
m
log
^2 m
nE
tn {Po2-\]
nE l"lJ
Since
the
v's
and
p0
are
completely independent
of each
other, this
equation
represents
the
dependence
of the
potential
difference
AII
between
metal
and
solution
on
concentration
and
hydrostatic
pressure.
It should
be
noted that the postulated forces
no
longer
appear
in the result. If
they
were
to appear,
the
hypothesis
posited in
§1
would
have been
carried
ad absurdum.
The equation
obtained
can
be
resolved into
two
equations,
namely:
(4)
n
RT
(aii)2- (An)
a
a
Tlog
£2
n
L^l.
n v
(An)
-
(An)
jn jn
...
{p
V
1
n
E
02
at constant
pressure,
at
constant
concentration.
The
final formula
(3)
could
have
also
been
obtained without the
hypothesis
proposed
in
§1
had the
external forces
been
identified with terrestrial
gravity.
However,
in that
case
v
and
p
would
not be
independent
of each
other
and
the resolution into
equations
(4)
would
not be permitted.