DOC.
34
193
electrons lead
to
a
formula for
black-body
radiation that contradicts
experience
n\
X
q,
(1)
^
=T.
Here
pv
denotes the density
of
radiation
at temperature
T
and
at
a
frequency between
v
and
v +
1.
What
is the
reason
that
Mr.
Planck did
not
arrive
at
the
same
formula,
but obtained instead the
expression
(2)
Pv
OtV°
o
T~
'
-
l
Mr.
Planck derived1 the
mean
energy
Ev
of
a
resonator
of
proper
frequency
v
situated in
a
space
filled with disordered
radiation
as
given
by
the
equation
[7]
(3)
-
_____ I. 1.1
-
LI
a
ii
`.1)
8iru2
This reduced the
problem
of
black-body
radiation
to
the
problem
of
determining
Ev
as
a
function of
temperature.
The
latter
problem
will
have
been
solved if
one can
calculate the
entropy
of
one
of
many
similarly
constituted,
mutually
interacting
resonators
of
proper
frequency
v
that
are
in
dynamic
equilibrium.
Let
us
envision the
resonators
as
ions that could
perform
rectilinear
sinusoidal vibrations about
an
equilibrium position.
The
fact
that the ions
have
electrical
charges
is irrelevant in
the calculation of this
entropy;
we
simply
have to
conceive these
ions
as mass
points
(atoms) whose
momentary
state
is
completely
determined
by
their instantaneous deviation
x
from the
equilibrium position
and
by
their instantaneous
velocity
dx/dt
=
£.
[5]
[8]
1M.
Planck,
Ann.
d.
Phys.
1
(1900): 99. [6]