374
DOC.
21
MOLECULAR MOTION IN
SOLIDS
involved.
It
is
possible
that
such
measurements,
with
deformation without
angular
deformation, would
lead
to values
of
k
significantly
different
from
those obtained
by
the
measurements
conducted thus
far.
At least
this
seems
highly
probable
from
the
theoretical
point
of
view.
[24]
§
4.
Remarks
about
the Thermal
Conductivity
of
Insulators
The result obtained
in
§1
makes it
seem
justified
to
attempt an approximate
calculation
of
the
thermal
conductivity
of
nonmetallically
conducting
solids.
If
e
is
the
mean
kinetic
energy
of
an atom,
then,
according
to
§1,
the
atom
releases
on
the
average
the
quantity
of
energy
a
.
t
to
the
surrounding
atoms
during
half of
an
oscillation
period,
a
being a
coefficient
of the
order of
magnitude
one,
but smaller than
one.
If
we
imagine
that the
atoms
are
arranged
in
a
lattice,
and consider
an
atom
A,
which lies
right
next to
an
imaginary
plane
that
does not intersect
any
molecule,
then the
atom A
will,
on
the
average,
send the
energy
X
•
•
Ebene
Fig.
2.
9
a-c
-
26
across
the
plane during
the time of half
an oscillation,
and thus the
energy
9
ae
•--2v
26
in
unit
time.
If d
is
the
smallest
distance between
neighboring
atoms,
then there
are
(1/d)2
atoms
per
unit
surface
area
abutting
one
side
of
the
plane,
and
together they
send
the
energy
9
1
a •-v
•-
c
13
d2
per
unit
surface
area
in
one
direction
(the
direction of
increasing x)
across
the unit
surface
area
of the
plane.
Since
the molecules
on
the other
side
of the
layer are
sending
the
quantity
of
energy
9
If
dt
,
-a
-
v-e
+--d
13
d\
dx
per
unit time
across
the unit
surface
area
in
the
negative
x-direction,
the total
flow
of
energy
will
be
9
1
dt
-a •-v
•
13
ddx