DOC.
12
COMMENT
ON EÖTVÖS'S
LAW
329
(1c)
5
=
k'
Let
us now
interpret
the
last
equation.
Let
S
(see
the
figure)
be
a
crosssection
of
a
grammolecular
cube
parallel
to
a
lateral
face.
2Uf
is
then
equal
to
the
potential
energy
(taken as
negative)
that
corresponds
to
the
totality
of the interactions between the
molecules
on
the
one
side
of
S
and
those
on
the other
side
of
S.
Ui
is
the
potential
energy
(taken
as negative)
that
corresponds
to
the interactions of
all
the molecules of
the
cube.1
The
most obvious
fundamental
hypothesis
concerning
the molecular
forces
that
leads
to
a simple
relation between
Uf
and
Ut
is
the
following one:
The
radius
of
the
molecule's
sphere
of
action
is
large
compared
with
the
molecule
but
is
of the
same
size for
different
kinds
of
molecules.
At
a
distance
r
two
molecules
exert
on
each
other
a
force whose
negative
potential
energy
is
given by
c2(r),
where
c
is
a
constant
characteristic of the
molecule,
f(r) is
a
universal
function of
r,
and
f(«)
is
equal
to
zero.
For
this
case
to
lead to
simple
relations,
f(r)
must be
so
constituted that
the
sums
representing
Uf
and
Ui
can
be
written
as
integrals;
we
will
assume
this
as
well
(with van
der
Waals).
We then obtain
by simple
calculation
[8]
4
Uf
=
cWK/1,
a
=
cWjV1.
[9]
Here
we
have
K1
=
J)dx,
extended
over
the entire
volume,
and
K,=
\fy(A)dA
0
where
oo
f
oo f oo
[10]
ifj
(J)
=
Jdx
J
Jf(r)
dydz.
[11]

oo

oo
1
There
is
a
noteworthy
inaccuracy
here, inasmuch
as certainly
not
all
of the
energy
Ui
can
be
designated as
potential
energy
in
the
sense
of
mechanics;
this would be
permissible only
if the
specific
heat
at constant volume would
be the
same
in
the
liquid
and in
the
gaseous
state.
It
would
surely
be
more
correct to
introduce the heat of
evaporation extrapolated
to
absolute
zero.