238
DOC. 10
RESEARCH
NOTES
of
[eq. 104]
is incorrect,
as
is its
reworking
[eq.
105]
(where
the crossed-out factor
2
should
be included). Presumably
at
a
later
stage
Einstein discovered his
error,
struck the factor
2,
and added
[eq.
106], correcting
the
first
term
in
the
right-hand
side of
[eq. 104]
to
[eq. 105]
and
[eq.
106].
[77]All
terms
are
combined
to
yield
[eq.
107]
for
(p,
which
is
incorrect
due
both
to
the
in-
correct
cancelation of
[eq.
105]
(where
the crossed-out factor
2
should
be
included) against
the last
term
of
[eq. 102]
and
to
the
disregarding
of the factor
1/4 in
front of
[eq.
102].
Pre-
sumably,
this factor
was
added
later.
[78]If
[eq.
108]
were
to
hold,
the
only
second-derivative
term remaining
in
(p
would
be
the
contraction with
gim
of the
only
second-order
term
Einstein
expected
in
his
gravitation ten-
sor,
namely
YKlYim,
Kl.
See
condition
(1)
in
the editorial
note,
"Einstein's Research Notes
on a
Generalized
Theory
of
Relativity."
[79]This
calculation
represents
a
continued evaluation of
the
incorrect
[eq. 107].
[p. 31]
Ka
^pß
3
Hnp
dg
rap 1
3Ypo
[80]
8
+
4
tY
K/ 3xk
dx/
[eq. 109]
KP^«
3*P
2 p
dxa
dxm
[eq.
110]
dyKI
3Yim
^
Kl
im
Kl im()x ()x
dxm
dxK
Sil
dxK dxm
[eq.
111]
k
ra
UAKUAm
32Yqß
i
I
m k
k
p
a ß
3xa3xß
d2y
Pß
8«?y™dxadxp
1
3\P
1
^Yv-rv
"
'Ka
3Y
pß
,,-y
'aß°
[81]
4gKPY«ß9x"9x
[eq. 112]
P
1
32Yk
1
aY,a
3YKß
1
32Y,q
1
32YKß
[eq.
113] 7.iK
=
4
-y'a
'aP5xa9xp
2
Bxß
dxa
+
27|CP9xa3xß
+
2y'ar)xadx^
L
^
J
x
a
[eq.
114]
[82]
d d
d\
P
d2y.
ha
3Y,"
1a
3Y,
'
'Kß
^Yia
^YKß
dx"
dxa
^'a^Kß^ y'adx"dxn
+
^^dxSdxo
+
3x".
dxa
dxn
dxa
P P P P P