184
REVIEW OF BROWNIAN MOTION
for
T
=
300.
Thus,
for the
body
to perform
fluctuations observable
under
the
microscope,
the force
acting
on
it
must not exceed
five millionths
of
a dyne
[13]
for
an
elongation
of
1
cm.
Let
us
add
one
further theoretical
remark to
the
equation
derived.
[14]
Suppose
the
body
under
consideration carries
an
electric
charge
distributed
over a
very
small
space, and
the
gas
surrounding
the
body
is
so
rarefied that
the
body
performs
sinusoidal oscillations
only
slightly modified
by
the
surrounding gas. The
body
then radiates electric
waves
into
space
and
absorbs
energy
from
the radiation of the
surrounding
space;
it thus mediates
an
exchange
of
energy
between
radiation
and
gas.
We
can
derive the
limiting
law
of
thermal radiation,
which
seems
to
hold for
long
wave
lengths
and
high
temperatures,
by
formulating
the condition that the
body
in
question
emits
on
the
average
as much
radiation
as
it absorbs.
We
arrive in
this
way1
at
the
following
formula
for
the radiation density
pv
that
corresponds to
the
frequency
v:
n
_
R
8lf2
m
Pp
-
N~TT
where
L
denotes the
velocity of
light.
The
radiation formula
given
by
Mr.
Planck2
reduces
to
this formula
at
low
frequencies and
high temperatures. From
the coefficient
of the
limiting
law
we can
determine the
quantity
N
and
thus arrive
at
Planck's determina-
tion
of
the
elementary quanta. The
fact that in the
way
indicated
we
do
not
obtain the
true
law
of radiation, but
only
a
limiting
law,
seems
to
me
to be
rooted in
a
fundamental
imperfection
of
our
physical conceptions.
We
will
also
use
formula (I)
to
decide
how
small the
suspended
particle
needs to be to remain permanently
suspended
despite the effect of
gravity.
We
can
confine ourselves
to
the
case
that the particle
has
a
greater specific
gravity
than the
liquid,
since the
opposite
case
is
completely
analogous.
If
v
is the
volume
of the particle,
p
its density,
p0
the
density
of
the
liquid,
g
the
acceleration of
gravity,
and
x
the vertical distance
of
a
point
from
the
bottom
of
the
container,
equation
(I) will
yield
[18]
[17]
[15]
1Cf. Ann.
d.
Phys. 17
(1905): 549,
§§1
and 2.
[16]
2M.
Planck,
Ann. d.
Phys.
1
(1900): 99.