372
THE
RADIATION
PROBLEM
10.
It
seems
difficult
to set
up a
theoretical
system
that
interprets
the
light quanta
in
a
complete
fashion,
the
way our
current
molecular
mechanics in
conjunction
with the
Maxwell-Lorentz
theory
is able
to
interpret
the radiation formula
propounded
by
Mr.
Jeans.
That
we
are
only
dealing
with
a
modification
of
our
current
theory,
not
with its
complete
abolition,
seems
already
to be
implied
by
the fact that Jeans'
law
seems
to be
valid
in
the
limit (for small
v/T).
An
indication
as
to
how
this modification
would
prob-
ably
have
to be
carried
out
is
given
by a
dimensional consideration
carried
[60] out
by
Mr.
Jeans
a
few
years
ago,
which
is
extremely important,
in
my
opinion,
[61]
and
which--modified in
some
points--I
shall
now
recount
in brief.
Imagine
that
a
closed
space
contains
an
ideal
gas
and
radiation
and
ions,
and
that
owing
to
their
charge,
the ions
are
able
to
mediate
an
energy
exchange
between
gas
and
radiation.
In
a
theory
of
radiation linked
with
the
consideration
of
this
system
the
following
quantities
can
be
expected to play
a
role, i.e.,
to
appear
in
the
expression to be
obtained for
the radiation
density
p:
a)
the
mean
energy n
of
a
molecular
structure (up to
an
unnamed
numerical factor
equal to
RT/N),
b)
the velocity
of
light
c,
c)
the
elementary
quantum
e
of
electricity,
d)
the
frequency
v.
From
the dimension of
p,
by
solely
considering
the
dimensions of
the
four quantities
mentioned above,
one can
then
determine in
a
simple
way
what
the
form of
the
expression
for
p
must
be.
Substituting the
value
of
RT/N
for
n,
we
obtain
f2
P
=
v3i(a)
,
where
/v
-
v
[62]
a
=
Nc
T
,
where
w
denotes
a
function that
remains
undetermined. This
equation
[63]
contains
the
Wien displacement law, whose
validity
can
hardly
still
be in
doubt. This
has
to be
understood
as a
confirmation
of
the fact that
apart
from
the four quantities
introduced
above,
no
other
quantities
having
a
dimension play
a
role
in
the radiation
law.