DOC
380
APRIL
1912 281
all of
the
duds. I discussed
everything
with
my
wife.
The
following
comments
are very
disorganized
and
very heterogeneous-simply
shavings,
and
important
to
us
only
insofar
as
each
comment
points
to
at
least
one,
even
if not
yet
dissected,
difficulty.
a)
Z
=
Apn1.[5]
Naturally,
this
formula
cannot
hold for
arbitrarily large
p,
because
Ap
must,
for better
or
for
worse,
remain smaller than
unity.
Of
course,
this
pedantic
objection
is
of interest
only
for
the
following
reason:
you
obtain the radiation
hv
JcT
formula
p
=
av3e
s
for
arbitrarily
large
p, i.e.,
Ts,
but for
large
Ts
and
p one
should
obtain the
Rayleigh-Jeans
formula.
Formally,
one
can,
of
course,
immediately make
the
initial
posit
that
leads to
Planck's
formula:[6]
Z
=
A(T)
ßv3
P
n1
(for
small
p:
Z
=
A(T)pn1),
p +
ßv3
and
for
p
=
oo
the
equation would,
in
fact,
take the
possible
form
Z
=
A (T)ßv3
·
n1
though
it would be
quite peculiar
if
A
depended
on T.
But
I
find this
solution
quite
unattractive because
it
is much
too
formal.
Informally,
one
would
seek
to find,
on
the
basis
of
a
somewhat
more special
model
of the mechanism of
decomposition,
a
modification of
the
eq.
Z=
A(T)pn1
(I)
which
remains reasonable
for
p
= oo,
and
see
whether
it
leads
to
a
reasonable radiation
formula. We
made
an
experiment
in
that
direction.
It
led
to
a
failure,
but it
is quite
remarkable that
it
leads
to
nonsense.-
The
idea
is
this: If
p
is made
larger
and
larger;
it
happens
more
and
more often
that
in
the
time interval
dt
a
molecule
is
hit
by
several
light
quanta.
This
is
akin
to
a
soldier
who
is
hit
by
two
or more
grenades,
even
though
he
can
die
only once.
Let
E,
=
number of
light
quanta
s passing
through
a
cm2 per
unit
time.
w
=
probability
that
an
individual molecule
of
the first kind will be hit
by an
individual
light
quantum
from
among
those
^
light
quanta.
(1-w)
=
probability
that
this individual molecule will be missed
by
that
individual
light
quantum.
(1-w)
=
probability
that
it will be missed
by
all
of
the
%
light
quanta-
1-(1-w)5
=
probability
that
such
an
incredible
thing
will not
happen
to
the
individual
molecule
(that is
to
say
that
it will be hit
by
at
least
one
of the
Ģ
light
quanta)
A(T)
=
probability
that
a
wounded molecule will die.
Z
= n1
.A(T)
.
(1
-(1
-
w)$)
=
mathematical
expectation
for
the number of
molecular deaths
in
unit
time
for
n1
molecules