136
DOC. 27 MAXWELL'S
EQUATIONS
{4}
{4}
[4]
{5}
{6}
{7}
-E
4
^
fivaßn
dF dF
+
sFgg^g^-jfF^
This, however,
can now
be written
as
i£[5
is
The first
one
of
these
terms
is,
in shorter
notation,
a
MV
and the second
one
is,
after differentiation and
some
rearranging,
-
\
E
9"^«"%
E
fivpr
a*
8
aßpT
Finally, taking
all four
of
the calculated
terms
together, one
obtains the relation
dg,
_
1V
f"°^v
2!v
=
«
v Mvt
o*
(8a)
where
s:
E
(-
s"
-
i
*%«:]•
(9)
8a
is the mixed tensor whose
components
are
1
or
0
depending upon
a
=
v or
a
*
v,
respectively.
A
comparison
of
equation (8a)
with
(42a)
l.c.
shows
that
(8a)
is the
energy-momentum
equation
of
the
electromagnetic
field,
where the
components
of
the
energy
tensor
are given
by
(9).
With the
help
of
(3)
and
(6)
it is
easily seen
that the
energy
tensor
of
the
electromagnetic
field found here coincides
with the
one
in the
previous theory.
However,
the
newly
found
form is
more
comprehensive
than the
one
found under the
previous
treatment of this
topic.
Additional
notes
by
translator
{1}
The
repeated typographical error
"yT"
in the German
original,
instead of
a
correct
"V," is
henceforth
corrected
in the translation without further note.
{2}
All summations
imply
that
\i,
v
are
summation indices and have been added
here.