DOC.
47 311
VT
=
*1
a
1
+
$
is the
(similarly
measured)
energy supplied
to
the
matter
per [108]
unit
volume
and
unit local time
r; 1/8n(X2 +
Y2...
+
N2)
is the
electromagnetic
energy
e
per
unit
volume, measured
the
same way.
If
we
take into
account
that
according
to
(30)
we
have to set
d/da
= [1

yE/c2]d/dt,
we
obtain
i
+
#]nTdt
+1
J
(i
+
$
e du)
=
0
This
equation
expresses
the principle of conservation of
energy
and
contains
a
very
remarkable result.
An
energy,
or
energy
input, that,
measured
locally, has
the value
E
=
edu
or
E
=
rj
dwdr, respectively,
contributes
to
the
energy
integral,
in addition
to
the value
E
that
corresponds
to
its
magnitude,
also
a
value
E/c2 yE =
E/c2
$ that
corresponds
to
its
position.
Thus, to each
energy E
in
the
gravitational
field there
corresponds
an
energy
of
position that
equals
the potential
energy
of
a
"ponderable"
mass
of
magnitude
E/c2.
Thus
the
proposition
derived in
§11,
that
to
an
amount
of
energy
E
there
corresponds
a
mass
of
magnitude
E/c2,
holds
not only
for the inertial but
also for
the gravitational
mass,
if the
assumption
introduced in
§17
is
correct.
(Received
on
4
December
1907)