184
DOC.
185 JANUARY
1916
or equal
to
{oBa}d(gotgBxdgyr/dxa)
or
equal to[5]
aß
a
dgor
For from
gpogor
=
6T
=
1 or
0 follows
dg/dx
goT
gpcr dx
,
xXy VS «X/
f-y
&
from
this
through
multiplication by
gox
analogously
also
gpXgaT
dgAt
OXa
dxa
It thus
follows[6]
dg° dg\T
gPxga
dXa
dx*
(ß)
(ß')
dL
=
aß
ra
dg°
aß
dgl\
a
ß
a
from which statement
(1)
follows.
From this it
follows
that the
gravitation
equa-
tions
can
be written in
the
form[7]
(2)
ÔL
dx* \dgl7 dgcr
=
-k(Tct
V
TT
-
-garT).
2yar
)...
2)
Conservation
laws.
If
you multiply
(2)
by
gßT,
then
you
obtain
upon
partial
differentiation
refor-
mulation
of
the
first
term,[8]
because of
interchangeability
of
a
and
ß,
a
V“
dL
-.gy
+
dL
dgaa
=
-kT"
dxa
dg°a
dg°
dg*
dx,
gg
dL
The
second
term
on
the
right-hand
side
disappears
because
dgT
dxe
dg0
ar
^Lfcrr
dxr-
dlgff
dxa
=
0.