DOC.
368 MARCH 1912 271
provided
that
=K
(5)
Uc/Ua
But in
(3)
and
(5)
K
is
the
ratio of
the rate constants
of the reaction and
counter-
reaction.
Thus,
as soon as
the
two
behave
like the
radiation
densities,
formula
(5),
follows, which,
for
the
case
considered,
is
identical
to
the
formula
I
used for
the
calculation
of the heat of reaction
from
the
frequencies.
Now I
take
the
more
general
case
a
+ b
=
c
The number of the
proper frequencies
is
now
three,
namely va,vb,vc.
The heat of reaction
now
becomes
Q
=
hvc-
1/2h(va + vb)
as
soon as
the
rate constant
for
the
reaction,
which
yields
c
from
a
+
b,
is proportional
to
ua
·
ub
The
proof
that
this
must
be
the
case
is not
yet
so
successful
that
I
would like
to present
it.
Let
me
express
the
essence
of
my
train of
thought
in
yet
another
way,
which
is
as
follows:
I
assume
that
two monochromatic
substances
are
in
equilibrium.
I
imagine
that
the
reaction
progresses
in
a
state
of
equilibrium.
I
state
now as a
thesis,
and therefore
arbitrarily,
that the isothermal
state
of
the
reaction
proceeding
infinitely slowly
at
equilibrium
can
be
brought
about
by
merely adding
and
removing
radiation;
and
I
further
state,
completely
relying
on
your
ideas
regarding
this
point,
that
every
substance
consumes,
or
releases,
a
definite amount
of radiation
during
its
conversion
to
a
converting
independent
mass
particle.
This
too is
an
arbitrary assumption.
Formula
(2)
then
follows
from the
two arbitrary
assumptions.
If
then,
once
again employing
your
ideas,
I
set
the ratio of
the
rate constants
again
equal
to
that
of
the
black-body
densities,
I
obtain formula
(4),
which
is,
in
essence,
identical
to
what I
stated earlier
concerning
the
connection between
the
heat of reaction
and the
proper
frequency.
The
conse-
quences to
be
mentioned,
apart
from
the earlier
published
numbers,
include
the
fact
that
according
to
what
has
been
said,
in the
case
of
optical
antipodes,
the
equilibrium
constant of whose
mutual
conversion
can
always
be
proved to
be
equal to one,
the
proper frequencies must
be
identical,
which fact
agrees
with
experience.
It
should
be
mentioned further that
the
normal
rate constants
of the substances
increase
geometrically
when
the
temperatures
increase
arithmetically,
which
is
also true
of radiation
density.
But this has
already
been
included in
your
presentations.
Your
investigations
on
gravitation[4]
fill
me
with amazement and
admiration,
and
your
announced
visit to
Berlin
fills
me
with
great
excitement.
I
will
come
to
see
you
as soon