240
DOC.
10
RESEARCH NOTES
C'
1
^
-
d2gim
d2gil
V
f
K' m
dxKdx,
dxKdxm
^YP°
i
m K
/ /
I K m
a
_P_
G
_
P
_
[86]
}
[eq. 121]
1
'dg*
d8
mo
d8im
^g
KP
5g/p
d8
[87]
Kl
dxt dxK
dxp
1
f
dyt
dy
V
•id
,
'mo
YmqSia
^Xm
Yip
8ma
0
0Y
\
+
P4
/
o
J
dyK/
v
?KpY,pg
dyK/
*/oY,
P
'podxK
+
Yp°~ax7
5lgG
lgG
=
0
gesetzt.
\X
-IY
4
I'mi
dxm
P
p
+
Y;lP
a?,,V
dx(
PG
dxc
dy 5Y.AK/'
'K/
I
SkP
-g-
+
S/p
j-
/
4YK'YjpYm9Ypa(^
+
0X
fdg/q
dg/q 9g,7V9gKP
3xoA
dgmp
+
3g
[88]
Km
m
3x
3x
l
4
A
3yPo
V
fy/
dym9
(
dx,
YP°g,a
+
rlr,
8^_
dxG
V
'?KP
3xm
Y"'?
+
gmP
9xk
Yk'
P =
'
3y^
r
pp
dx/
dyKl
g
V
KP
dxm
Yma
^moYK/
I
=
p
dy dy4/'
*mq
Ki
sKmymq
)
K
=
?
p 3x^
5x
dYpq/
dx"
g
KP
?Ymq
_
dYKl
Kp
3x."
^m(i
+
^mP^KP
dx"
dx
m K
+
zu
umständlich.
[85]Einstein begins
an
incomplete attempt
to
expand
[eq. 120],
the
fully
contravariant form
of the Ricci
tensor.
[86][Eq.
121]
is
the Riemann
tensor
with its second-derivative
terms
reduced
to two
in
a
manner
admissible
in
the formation of the
fully
contracted
curvature
scalar
(see
[p.
28];
see
[eq.
91]
on [p.
27]
for the full form of this
tensor).
[87]Einstein
commences
expansion
of the contracted form of the
first
term
of the
summa-
tion
in
[eq.
121].
[88]Einstein
commences
expansion
of the contracted form of the second
term
of the
sum-
mation
in
[eq. 121].