10
PHENOMENA OF
CAPILLARITY
can
be
considered
unhesitatingly
as
infinitesimally
small; likewise,
compres-
sions
in
our
experiments
are very
nearly proportional
to
the
compression
forces applied.
Thus,
the
phenomena
proceed
as
if the
compression
forces
were
infinitesimally
small. If this is taken into
account,
then
our
equation
reduces
to
[20] X.dp
=
-
T.a.dp
.
If
we now
apply
the
assumption
that the kinetic
energy
of
the
system
does not
change
in isothermal
compression,
we
obtain the
equation
X.dp +
work
of
compression
+
work
of the molecular forces
=
0.
If
P
is the
potential of
the molecular forces, then the last-mentioned
work
is
[21]
liv
•dp
If
one
inserts herein
our
expression
for the
magnitude
of the
potential
of the molecular forces
and
takes into
account
that the
work
of
compression
is
of
the order
dp2,
one
obtains,
neglecting
this
quantity which
is
infinitesimally
small
of second order,
[22]
(s02a'
a
_
v
where
K
denotes
the
compressibility
coefficient
in
absolute units.
We
thus
obtain
once more a means
for the determination of the looked-for
proportional-
ity coefficient for the
quantities
ca.
I
took the
a
and
k
values for the
[23]
temperature
of ice
from
Landolt
and
Börnstein's tables.
This yields
the
following
values for the factor
sought:
Xylene
Cymene
Turpentine
oil
Ethyl
ether
1.71
x
104
Ethyl
alcohol
1.70
x
104
1.71
x
104
Methyl
alcohol
1.74
x
104
1.73
x
104
Propyl
alcohol
1.82
x
104
1.70
x
104
Amyl
alcohol 2.00
x
104