DOC.
4
THEORY OF STATIC GRAVITATIONAL
FIELD
113
consequence
of
equations
(1a).
It should be noted that the
quantity
1/2(S2
+
S2),
rather than the actual
energy density
c/2
(S2
+
S2),
is what determines the
gravitation
of
an
electromagnetic field, i.e.,
is
equivalent
to
spatial density
of
stationary
inertial
mass.
This
is
also
to
be
expected,
because the
expression
1/2(@2+
S2) is
the
energy density as
it
appears
to
an
observer
doing
measurements
with
a
"pocket
instrument." It is therefore this
quantity
that
is
analogous
to
the inertial
mass,
according
to
the definition of the latter used
by
us.
It follows from these
arguments
that there
is also,
conversely, a
reaction of
the
electromagnetic
field
on
the
gravitational field,
the
expression
of which for the static
case
follows
immediately
from the
arguments presented,
since the
spatial
function
2 2 1/2(@+s)
is
equivalent
to
an
especially large density
of
unmoving ponderable
mass.
However, I
will
not
deal further with this here.
Likewise,
I
will
not
deal here
with the law
concerning
the
bending
of
light
rays
in the
gravitational
field,
which
is
contained in
equations (1a),
because this has
already
been
given
to
a
first
approxima-
tion in the
paper
on
the
same topic published
last
year. [17]
§3.
Thermal
Quantities
and
the Gravitational
Field
[18]
Let
two heat reservoirs
W1
and
W2
be
set
up
in
two
separate
locations
at
which the
velocities
of
light
are
c1
and
c2,
respectively.
Let the
two have the
same
temperature
insofar
as
the
same
thermometer
("pocket
thermometer"),
brought
into
contact
with
the
two
one
after
another,
shall have the
same
temperature ("pocket-thermometer"
temperature)
T*
in
both
cases.
By "temperature" (T) simpliciter
we
will understand
the
temperature
as
defined
by
Carnot
cycles.
We
inquire
into the
relationship
that
exists between the
temperatures
of the heat
reservoirs,
W1
and
W2.
Imagine
the
following cyclic process.
A
body
with the
pocket temperature T*
withdraws the
pocket
heat
quantity
Q*
from
reservoir
W1
and
is
then moved to
reservoir
W2.
This
same pocket-heat-quantity Q*
is then transferred from the
body
to
heat reservoir
W2
at the
pocket temperature T* and, finally,
the
body
is
moved
back
to
the reservoir
W1.
According
to the results of the
previous paper,
the heat
actually
withdrawn from
one
reservoir and
supplied
to
the
other
is
Q1 =
Q*
c1,
[19]
Q2 =
Q*
c2.
The well-known relation
Q1
=
Q2
T1 T2
therefore
yields
at
once