DOC.
12
COMMENT ON EOTVOS'S
LAW
331
such molecules
M
lie
directly
below
the
surface
S,
the
potential
energy,
which
we
denoted
above
by
2Uf,
will
be
given by
2Uf =
9
.N.p.
Thus,
we get
Uf
=
-N-1/3,
Ui
26
or,
if
we
substitute the
value 7
.
1023
for
N,
Uf
=
3-10"9.
Ui
On the other
hand, I
calculated the
constant
k'-which,
according
to
(1c),
should be
identical
to
the
value
just
obtained-for
mercury
and
benzene
from
experimental
data
by means
of the
empirical
equation
(1b),
and
obtained
the
values
5.18
.
10-9
5.31
10-9.
This
order-of-magnitude agreement
with
the
value
obtained
by
the
rough
theoretical
argument presented
above
is
very
remarkable.
Stimulated
by an
oral remark
by my
colleague
G.
Bredig,
I also
pondered
what
the
[16]
order of
magnitude
of
the
theoretically
obtained
value
of
Uf/Ui
would
be
if
one
assumed
that the molecule interacts
not
only
with its
immediate
neighbors,
but
also with
molecules
that
are
farther removed. The
cube
that contains the molecules
in
interaction
with
one
molecule will
then
have
n3
rather than
33
molecules.
In that
case
Uf/Ui
comes
out
nearly proportional
to
n.
Thus, one
still
obtains
a
value
for
Uf/Ui
of the
right
order
[17]
of
magnitude
for
n
=5
or
n
=
7. Nevertheless,
it
is
highly
probable
that
a
molecule
interacts
only
with its
immediate
neighbors,
because
it must
be considered
as
very
improbable
that the
radius
of the
molecular
sphere
of
action would
be
proportional
to
the
cubic
root of
the
molecular volume
without
depending
otherwise
on any
physical
constant
of the
molecule.
There
is
one more
remark that
comes
to mind in
connection
with this
argument.
We
know
that
substances with
very
small
molecules
deviate
considerably
from the
law
of
corresponding
states. Should this not be
related
to
the
fact
that the radius of the
molecular
sphere
of
action
of
such substances is
more
than three
times
as large as
the
molecular radius?
(Received
on
30
November
1910)
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