88 HEURISTIC
VIEW OF
LIGHT
For
the time
being,
we
disregard
the
radiation emitted
and
absorbed
by
the
resonators and look
for the condition for
dynamic
equilibrium
corresponding
to
the interaction
(collisions)
of molecules
and
electrons.
For
such
an
equilibrium,
the kinetic
theory
of
gases
provides
the condition that
the
mean
kinetic
energy
of
a
resonator
electron
must
be
equal
to
the
mean
kinetic
energy
of the progressive motion
of
a gas
molecule. If
we
resolve the
motion of
the
resonator
electron into three
mutually
perpendicular oscillatory
motions,
we
find for the
mean
value
E
of
the
energy
of
such
a
linear
oscillatory
motion
Al
-
3 N
where
R
denotes the
universal
gas
constant,
N
the
number
of
"real
[10]
molecules" in
one
gram-equivalent, and
T
the absolute
temperature,
for
because
of
the
equality
of the time
averages
of
the resonator's
kinetic
and
potential
energies,
the
energy
E
is
2/3
times
as
large
as
the kinetic
energy
of
a
free
monoatomic
gas
molecule. If
due
to
some
factor--in
our
case,
due to
radiation--the
energy
of
a
resonator
were
to have
a
time
average
larger
or
smaller than
E,
the collisions with the free electrons
and
molecules
would
lead
to
an
energy
transfer
to
the
gas
or an
energy
absorption
from
the
gas
that
is,
on
average,
different
from
zero.
Thus,
in
the
case we are
consider-
ing,
dynamic
equilibrium
is
possible
only
if the
mean
energy
of
every
resonator
equals E.
We
now
apply
similar
reasoning
to
the interaction
between
the
resonators
and
the radiation
present
in
the
space.
Mr.
Planck
has
derived
the condition
for the
dynamic
equilibrium
in
this
case1
using
the
assumption
that
[11]
1M.
Planck,
Ann.
d.
Phys.
1
(1900):
99.