238 DOC. 20 THEORETICAL ATOMISM
to
maintain this motion associated with
constant
sliding.
For
a given
motion,
this
expenditure
of work
depends
on
the
nature
of the substance and
on
its
physical state;
the
physicists
have therefore defined
a
characteristic
constant
dependent
on
the
physical
state
(the viscosity coefficient)
that
determines
the
forces that the
gas layers
sliding along
each other
exert
on
each other. The kinetic
theory explains
this friction
resistance
in the
following way.
If
we
could
see
the motion
of
the individual
molecules
in
the
tube, then,
in
every
small volume element this motion would have
to
look
to
us
like,
say,
the motion of
mosquitos
in
a
mosquito
swarm.
Suppose
that,
in
addition
to
the motion of the individual
mosquitos
of the
swarm,
it
were
also
possible
to
perceive
the motion of the
mosquito
swarm as a
whole.
Only
a
motion of
the latter kind
can
be
perceived
by an
observer who does
not
perceive
the individual
mosquito.
If
the
swarm moves as a
whole, then, to be sure,
the individual
mosquito
possesses
a
motion
of
arbitrary magnitude
and
direction,
but if
one
simultaneously
keeps
one's
eye
on
a great
number of
arbitrarily
chosen
mosquitos
in the
swarm,
then
they
are moving on
the
average
in
the direction of the motion of the
swarm.
Let
us now
consider the central
part
of the
tube,
in
which the "swarm motion"
is
greatest along
the direction of the
axis!
Due
to
the molecular
motion,
this central
part
will
exchange
molecules with the
outer
part
without cessation.
However,
since
the
newly entering
molecules
come
from
parts
with lesser
swarm
motion,
their motion
along
the direction of
the
axis of
the
tube
will,
on average,
be smaller than that
which
corresponds
to
the "swarm motion" of the central
part.
Thus,
the
velocity
of the
swarm
motion of the central
layer
would decrease if
one
had
not
seen
to it
that the
swarm
motion be maintained
or, more accurately, produced anew
all the time
by
an
external effect such
as,
for
example,
the
pressure
difference
acting
at
the
ends
of
the
tube.
Thus
one can see
that
a
steady application
of force and
energy
is
needed
in
order
to
maintain the motion.
In the
mathematical
investigation
of
the
process,
a
fundamental role
is
played
by
a
concept
that
did
not appear
in the
previous
considerations,
namely
the
concept
of
the
"mean free
path."
It
turns out
that,
under otherwise
identical
circumstances,
the
energy
needed
to
maintain
a
given
flux
is
greater,
the
greater
the
path
that,
on
average,
a
molecule
traverses
between
two
collisions(the
mean
free
path).
The
theory permits
the
calculation of
the
mean
free
path
from the
observed value of
the
viscosity;
for
air
at atmospheric
pressure,
this
path
is
about
equal to
a
ten-thousandth
part
of
a
millimeter.
It
increases with
the
inverse value of
the
gas
pressure.
[5]
In
conformity with experiment, the theory produces the amazing result that, for
a
given motion, the expenditure of work per second that
is
needed
to
maintain
this
motion
is
independent of the gas pressure
(cf.
Article
11, p.
233).
Consider
a
gas
in
which the temperature,
i.e., the
intensity of thermal agitation,
varies with the height. Let the temperature
be
highest
at
the top and gradually
Thermal Con-
duction
in
a
Gas.