360
THE
RADIATION
PROBLEM
According
to
Maxwell's
theory,
an
ion
capable
of
oscillating about
an
equilibrium
position in
the
direction
of
the
X-axis will,
on
the
average,
emit
and
absorb
equal amounts
of
energy
per
unit time
only
if
the
following
relation holds
between
the
mean
oscillation
energy Ev
and
the
energy
density
of
the radiation
pv
at
the
proper
frequency
v
of
the oscillator:
[10]
h-TSV'v-
(I)
where
c
denotes
the
speed
of
light. If
the
oscillating
ion
can
also
interact with
gas
molecules (or,
generally,
with
a
system
that
can
be
described
by
means
of
the molecular
theory),
then
we
must
necessarily
have,
according
to
the statistical
theory
of
heat,
RT
L
=
X
(II)
v
(R
=
gas
constant,
N
=
number
of atoms
in
one gram-atom,
T
=
absolute
temperature),
if,
on
the
average,
no
energy
is transferred
by
the oscillator
from
the
gas
to
the radiation
space1.
From
these
two equations
we
arrive
at
p, -1 "2?-
(III)
i.e., exactly the
same
law
that
has
also
been found
by
Messrs.
Jeans
and
H. A.
[12]
Lorentz2.
3. There
can
be
no
doubt, in
my
opinion,
that
our
current
theoretical
views inevitably
lead
to
the
law
propounded
by
Mr.
Jeans.
However,
we can
consider it
as
almost
equally
well established that formula
(III)
is
not
[11]
[13]
[14]
1M.
Planck,
Ann. d.
Phys.
1
(1900): 99.
M.
Planck,
Vorlesungen
über die
Theorie
der
Warmestrahlung
[Lectures
on
the
theory
of
thermal
radiation],
Chapter
3.
2It should
be
explicitly
noted that
this
equation is
an
inevitable
consequence
of
the statistical
theory
of
heat.
The
attempt,
on
p. 178
of the
book
by
Planck just cited,
to question
the
general
validity of
Equation
II,
is based,
it
seems
to
me,
only
on a
gap
in Boltzmann's considerations,
which has been
filled
in
the
meantime
by
Gibbs'
investigations.