230
REMARKS
ON
BROWNIAN MOTION
2.
We
will
now
examine whether
there is
any
chance
of actually
observing
this
enormous
velocity
on a
suspended
particle.
If
we
did
not
know
anything
about
the molecular
theory
of
heat,
we
would
expect the
following:
If
we
imparted
a
velocity
to
a
particle
suspended
in
a
liquid
by
an
impulse
of
an
external
force, this
velocity
would
be
rapidly
used
up
through
the friction
of
the
liquid.
We
neglect
the latter's inertia
and
bear in
mind
that
the resistance
experienced
by
the particle
moving
with
velocity
v
is 6ikPv,
where
k
denotes
the coefficient of
viscosity of
the
liquid and
P
the radius
of
the
particle.
We
get
the
equation
[7] m
tjjj
=

6ikPv.
This yields for
the time
o
in
which
the velocity decreases
to
one
tenth
of
its initial value
a

ä
v
~
0AM6ikP
'
For
the
platinum
particle (in
water) mentioned
above,
we
have to
put
[8] P
=
2.5.106cm,
and
n
=
0.01,
so
that
we
get1
=
3.3.107 seconds.
Returning
to
the molecular
theory of
heat,
we
must modify
this analysis.
True,
we
must
assume now
as
well that,
due
to
friction,
the
particle
loses
almost all its initial
motion
during
the
very
short time d.
But
we
also
must
assume
that
during
this time the
particle
receives
new
impulses
by
a
process
that
is the
reverse
of internal
friction,
so
that it retains
a
velocity
that
on
the
average equals
v2.
But
since
we
must
imagine
that
the
direction
and
magnitude
of
these
impulses
are
(almost)
independent
of the
initial direction
of
motion and velocity of
the particle,
we
must
conclude
that
the velocity and
1For "microscopic"
particles
$
is significantly
greater
since,
under other
wise equal
conditions,
§
is
proportional to
the
square
of
the radius
of
the
particle.