DOC. 30 FOUNDATION OF GENERAL RELATIVITY
191
the
special case
of
the restricted
theory
of
relativity
;
and
in
addition
J1
=
jx, J2
=
jy,
J3
=
jz,
J4
=
P,
we
obtain in
place
of
(63)
^-+ i
=
curl
H'
(63a)
div
E'
=
p
J
The
equations
(60), (62),
and
(63)
thus
form
the
generali-
zation
of Maxwell's field
equations
for free
space,
with the
convention
which
we
have established with
respect
to the
choice
of
co-ordinates.
The
Energy-components
of
the
Electromagnetic
Field.-
We form the inner
product
ko
=
FouJu
....
(65)
By
(61)
its
components,
written
in the three-dimensional
manner,
are
=
pTSx
+
[j
.
H]x
-
O'E)
.
(65a)
Ko
is
a
covariant
vector
the
components
of
which
are
equal
to
the
negative
momentum,
or,
respectively,
the
energy,
which
is
transferred
from
the electric
masses
to
the
electro-
magnetic
field
per
unit
of
time
and volume.
If the
electric
masses
are
free,
that
is,
under the
sole influence of the
electromagnetic field,
the covariant vector
ko
will vanish.
To
obtain the
energy-components
Tvo
of
the
electromagnetic
field,
we
need
only
give
to
equation
ko
=
0
the form
of
equation
(57).
From
(63)
and
(65) we
have in
the
first
place
K
=
Y**
-
=
-
(F
FM")
-
*
Ix.
av
)
*
?)Xr
•
The
second
term
of
the
right-hand side, by
reason
of
(60),
permits
the transformation
-
-
u-rv-tt-