90 HEURISTIC
VIEW OF
LIGHT
[16]
This relation, obtained
as
the condition of
dynamic
equilibrium,
not only
fails
to
agree
with
experience
but it also
states
that
in
our
model
a
definite
distribution
of
energy
between
ether
and matter
is
out
of the question, since
the wider the
chosen
range
of
the resonators' frequencies, the
larger
the
radiation
energy
of
the
space,
and
we
obtain in the limit
[17]
"00
0
p
du
R 8?r
N
Z*
fOO
0
v2dv
-
oo
[18]
§2.
On
Planck's determination
of
the
elementary
quanta
We now
wish to
show
that
Mr.
Planck's
determination of the
elementary
quanta
is
to
some
extent independent of
his
theory
of
"black-body
radiation."
Planck's
formula1
for pv,
which has been
sufficient
to account
for all
observations
made
so
far, reads
[20]
Pv
~
'
e
-
1
where
a
=
6.10
x
10-56
ß
=
4.866
x
10-11
.
For large
values
of
T/v,
i.e.,
for
large
wavelengths
and
radiation densities,
this
formula reduces
in
the limit
to
=
I
v2T.
One
can see
that this formula
agrees
with that
derived
from
the
Maxwellian
theory
and
the electron
theory
in
§1.
By
equating the
coefficients
of
the
two
formulas,
we
obtain
[19]
1M.
Planck,
Ann.
d.
Phys.
4 (1901):
561.