DOC.
34
195
where
AH
should be chosen
very
small,
yet
large
enough
to make
R lg(AH)/N
a
negligible
quantity.
S
is then
independent of the
value of
AH.
If
one
substitutes the variables
xa
and
ta
of
the
resonators
instead
of
dp1,...dpn
in the
equation and
takes into
account
that the
equation
holding
for
the
a-th
resonator
is
rE+dE
dxdf
=
const.
dE''
£
a a a
a
(because
Ea
is
a
quadratic,
homogeneous
function of
xa
and
£a),
one
obtains the
following expression
for
S:
(5)
S
=
l
lg
¥
,
where
one
has
put
(5a)
V
=
H+MI
H
dE....
dEn
.
1
n
If
one
would
calculate
S according
to
this
formula,
one
would
again
arrive
at
the invalid radiation formula (1).
To
arrive
at
Planck's
formula,
[15]
one
has to
postulate
that,
rather than
assume any
value whatsoever, the
energy
Ea
of
a
resonator
can
only
assume
values that
are
integral multiples of
e,
where
e
~
71 '
This is
because,
on
setting
AH
=
e,
one immediately sees
from
equation
(5a)
that,
except
for
an
inconsequential
factor,
W
turns
into the
very
quantity
that
Mr.
Planck
named
"the
number
of
complexions."
[16]
Hence,
we
must
view
the
following
proposition
as
the basis
underlying
Planck's
theory
of radiation:
The
energy
of
an
elementary resonator
can
only
assume
values that
are
integral multiples of
(R/N)ßv;
by
emission
and absorption, the
energy
of
a
resonator
changes
by jumps
of integral multiples of
(R/N)ßv.