204 DOC.
10
RESEARCH NOTES
[5][Eq. 3]
is
a
reworking
of
[eq.
2].
[6][Eq. 4]
is
the condition
for
a
stationary gravitational field in
coordinates
naturally adapt-
ed
to
the
field.
If
Div is
the
four-divergence (see, e.g.,
Doc.
1, [p.
54];
the abbreviation Div
is
used
in
Laue
1911a,
p.
70) and
T
the
coordinate
independent
tensor represented
by
the matrix
G^,
the condition
Div
T
=
0
would be
a
natural candidate for
an
invariant form of condition
[eq. 4].
Its
component
form
in arbitrary
coodinates
is
[eq. 5]
and
it would be invariant if
[eq.
6]
holds for
arbitrary a.
[7]In
the
following,
G^
is transformed
in
the two-dimensional
case.
[p.
3]
AAp)
grad2 grad2 grad2
grad2p
2.
Ordnung
grad2~)
grad2A
(~
4.
Ordnung
(d2
I
+
ay2
`~ax2
ay2
(~
d~
a2 a2
I
+
a?
I~ax2
ay2
a4 a4
÷2
+ =
ax2ay2
____
+
+
ax
gradç
grad
A
p
ax
+
Diie
ersten
2
Schritte
2
Dimensionen
[8]
[9]
[eq. 7]
System
der
G
äquivalent
dem
System
a2Q~-
OX^OXv
Gleichung
soll
so
sein,
dass
in
jedem
Glied nach allen
x
gleich
oft diff.
wird.
Linear
unmöglich von
8. Ordnung
in
(p