180
REVIEW OF BROWNIAN
MOTION
Doc. 32
ON
THE
THEORY OF BROWNIAN MOTION
by
A.
Einstein
[Annalen
der
Physik
19
(1906):
371-381]
Soon
after the
publication of
my
paper
on
the
motion
of
particles
[2] suspended
in
liquids
demanded
by
the molecular
theory
of heat,1
Mr. Siedentopf
[3] (Jena) informed
me
that
he and
other physicists-Prof.
Gouy
(Lyon)
probably
having
been
the first-had
become
convinced
by
direct observation that the
so-called
Brownian motion
is
caused
by
the
random
thermal
motion
of the
liquid's molecules.2
Not only
the qualitative
properties of
Brownian motion
but also the order of
magnitude
of
the
paths
traversed
by
the
particles
are
in
full
agreement
with the results of the
theory.
I
shall
not
compare
here the
meager
experimental
material available
to
me
with the results of the
theory,
but shall leave this
comparison
to
those
engaged
in
experimental investigation
[5]
of
this topic.
The
present
paper
shall
supplement
my
above-mentioned
paper
in
several
points.
We
will derive here
not only
the translatory, but
also the rotational
motion of
suspended
particles for the
simplest
special
case
when
the
particles
[6]
have
a
spherical
shape.
We
will also establish
the shortest observation times
for
which the result
given
in the
paper
is still
valid.
We
will
use
here
a more
general
method
of derivation,
partly
to
show
how
Brownian motion
relates
to
the
foundations of the molecular
theory
of heat,
and
partly to be
able
to
derive the
formulas for
the
translatory
and
for the
rotational
motion
by
a common
investigation.
Let
us assume
that
a
is
an
observable
parameter
of
a
physical
system
in
thermal
equilibrium and that
the
system
is
in so-called indifferent
equilibrium
at every
(possible) value of
a.
According
to
classical
thermodynamics,
which
makes
a
fundamental
distinction
between
heat
and
other kinds
of
energy,
spontaneous
changes
of
a
do not
take
place, but
according to
the molecular
theory
of heat
they
do. In
the follow-
ing
we
will
investigate
what
laws
these
changes
must obey according to
the
[1]
[4]
1A.
Einstein,
Ann.
d.
Phys.
17
(1905): 549.
2M. Gouy,
Jour.
de
Phys.
7,
No. 2
(1888):
561.