330
DOC.
12
COMMENT
ON
EÖTVÖS'S
LAW
Thus,
K1
and
K2
are
universal constants
that
depend
only on
the
elementary law
of
molecular
forces.
From
this
one
obtains
(2)
-L
=
*V"3,
[12]
in
contradiction
to
(1c),
the
equation
to
be
regarded
as
expressing
the results of
experience.
Even
without
any
calculation
one can see
that, neglecting
the
universal
factors,
the ratio of
Uf
to
Ui
must
be the
same as
the ratio of the radius of the
molecu-
lar
sphere
of
action to
the
edge
of
the
gram-molecular
cube
(v1/3).
Thus,
if the
radius of
the
sphere
of
action
is universal,
one
cannot arrive at
equation
(1c)
but
only
at
equation
(2).
It
can
easily
be
seen
that,
in
case
equation
(2)
were valid,
it would be
impossible
to
[13]
draw
a
conclusion about the molecular
weight
of
a
liquid
from
the
capillarity
constant.
To arrive
at
equation
(1c), one
must start
from the
assumption
that the radius of
the
molecular
sphere
of
action
is proportional
to
the
quantity
v1/3
or,
what amounts to
the
same,
to the distance between
neighboring
molecules
of the
liquid.
This
assumption
seems
rather absurd
at first
sight,
because
what
should the radius of
the
sphere
of
action
of
a
molecule
have to
do
with how
far
away
the
neighboring
molecules
are
situated? The
supposition
becomes reasonable
only
in
the
case
when
only
the
neighboring
molecules,
but
[14]
not
those farther
removed,
are
within
the
region
of
action
of
a
molecule.
In that
case,
in
accordance
to what has
been
said
above, equation
(1a)
must
be
obtained, and
we are
even
in
a
position
to
estimate the
value
of
the
constant
k'. The
argument
to
that
effect,
which I
am
now
going
to
present,
could
probably
be
replaced
by
a more
exact
one;
but
I have
chosen
it
because
it makes do with
a
minimum
of
formal
elements.
Let
me
conceive
of
the molecules
as being
regularly
distributed
in
a quadratic
lattice.
In
this lattice I
consider
an elementary cube,
the
edges
of
which
contain three
molecules
each, so
that the entire
cube
contains
33
=
27 molecules.
One of them
is
in
the
center.
The other
26,
and
only
these,
I
consider
as
neighboring
the molecule
in
the
center,
and
[15]
I make
my
calculation
by assuming
that
they
are
equidistant
from
the central
molecule.
If the
potential
energy
(taken
as
negative)
of
a
molecule
with
respect
to
one
of
its
neighbors
is
denoted
by
p,
then
its
potential energy
with
respect
to all
the
neighboring
molecules
is
equal
to
26p,
and hence
U.
=
-N-26y.
If
we,
further,
imagine
that
our
central molecule M
lies
immediately
below
the
plane
S in
the
figure,
and that the
boundary
surfaces
of the
gram-molecular
cube
depicted
there
are
parallel
to
the lateral
faces
of
the
elementary
cube
of
the
molecular
lattice,
then
our
molecule M
is
in
interaction
with 9
molecules of the
next-upper
layer.
Since
N2/3