392
CONSTITUTION
OF
RADIATION
Assuming
for
an
instant that
the above
took full
account
of the
mechanical effect
of
radiation
on
the plate,
we
arrive
at
the
following
interpretation.
Through
collision with
gas
molecules,
impulses
of
random
direction
are
imparted to
the
plate
at random
intervals.
The
velocity of the
plate
always
decreases
between
two
such
collisions because
of
radiation
friction,
and
kinetic
energy
of
the
plate
is converted into radiation
energy.
Consequently
the
energy
of
the
gas
molecules
would
continually
be
converted
into radiation
energy
by means
of the plate until all the
energy
had
turned
into radiation
energy.
Hence
no
equilibrium
could exist
between
gas
and
radiation.
This
consideration is
faulty
because
one
cannot
consider the forces
of
pressure
exerted
on
the
plate
by
radiation
as
constant
in time
and
free
of
random
fluctuations,just like the forces
of
pressure
exerted
on
the plate
by
the
gas.
For
thermal
equilibrium to
be possible, the fluctuations
of
the
radiation
pressure
must
be such that
on
the
average
they
compensate
for
the
velocity
losses
of the plate
caused
by
radiation
friction,
where
the
average
kinetic
energy
of
the plate
equals
one-third
of
the
average
kinetic
energy
of
a
monoatomic
gas
molecule. If the
law
of
radiation
is
known,
one can
calcu-
late the radiation
friction,
and
from
this
one
can
calculate
the
average
value
of the
momenta
imparted
to
the
plate
due
to
fluctuations
of the
radiation
pressure
so
that
statistical
equilibrium
can
exist.
This consideration
becomes
even
more
interesting if the
plate
is
chosen
such
that
only
radiation
of the
frequency
interval
dv
is
completely
re-
flected,
while radiation
of
other frequencies
passes through
without
absorp-
tion;
then
one
obtains the fluctuations of the radiation
pressure
for
the
radiation in the
frequency
interval
dv. I
shall
now
present
the result of
the calculation for this
case:
If
A
denotes the
momentum
transferred
to
the
plate
during
time
r as a
result
of
the
irregular
fluctuations
of
the
radiation
pressure,
one
obtains for the
mean
square
of
A
the
expression
a*
=
I
hpv +
fc
&
dvfr
This
expression,
first
of
all, is
conspicuous
by
its
simplicity;
there
is
not
likely
to
exist another radiation formula
agreeing
with
experience
within the
range
of experimental
error
that presents
such
a
simple expression