DOC.
14
EINSTEIN AND BESSO MANUSCRIPT
363
[p.
2]
(Einstein)
(2)
[6]On
[p. 2], [eq.
16]
for
g44
is
derived
with
the
help
of the
"Entwurf"
field
equations
in
the form
-Duv
=
K(tuv
+
Tuv)
(for
a
possible
motivation for
this calculation,
see
note 78).
The
44-component
of
this
equation
states that all
second-order
terms in -D44(g)
-k
t44
(see
[eq. 12])
cancel
one
another.
In
[eqs.
8-11],
the various second-order
terms in
this
expression
are
evaluated
(the
expression
is
similar
to
eq. (2)
in
the editorial
note,
"The
Einstein-Besso
Manuscript
on
the Motion of the Perihelion of
Mercury").
First, -D44(g) is
dealt
with.
The
(2)
second-order contribution
to this term
can
be written
as
the
sum
of three
terms:
Ag44,
and the
second-order contributions to
[eq. 9]
and
[eq.
10]
(with u
=
v
=
4).
The minus
sign in
front of
[eq. 10]
should
be
a plus
sign.
These
contributions
are
evaluated with the
help
of
the
first-order
metric
given
in
[eqs.
4-5]
on [p.
1]
and
at
the
top right
corner
of
[p.
2].
The
three
expressions
under
[eq. 9]
all should have
a
plus
instead of
a
minus
sign.
With
the results found for the
terms
in
[eq.
9]
and
[eq.
10],
-D44(g)
turns into
[eq. 8].
Because of
the
sign
error
in
[eq.
10],
the
last
term
of
[eq. 8]
should
have
a
minus instead of
a
plus
sign
(the
sign error
in
evaluating
[eq.
9]
is
corrected
in
[eq.
8]).
Next,
the second-order contributions
to
-Kt44
are
evaluated
(see
[eq.
11],
u
= v
=
4). Inserting
the results found for
-D44(g)
and
-Kt44
into
[eq. 12], one
arrives
at
[eq.
13].
Because of
the
sign
errors
in
[eq.
10]
and
[eq. 8],
the factor
5/4
in
[eq. 13]
should be
-3/4.
(2)
[7]In
[eq.
14]
the
assumption
is
made that
g44
is
of
the
form a/r2,
with
a a
constant.
Inserting
(2)
this form of
g44
into
[eq.
13],
one
arrives
at
[eq.
15],
from which
a
can easily
be
determined.
[8]Inserting the value found for
the constant
a
(see note
7)
into
[eq.
14], one
arrives
at
[eq.
16]
(2)
for
g44.
Because of the
error
in
[eq.
13]
(see
note
6),
the factor
-5/8
should
be
3/8,
in
agreement
with
[eq.
42]
for
guv on [p. 6].
[9]The
material
in
the lower
right
corner
is in
Besso's hand.
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