DOC.
14 EINSTEIN AND BESSO MANUSCRIPT
371
[p. 6]
(Einstein)
[25]Inserting [eq. 17]
into
[eqs.
20-22], all
on [p.
3],
one
arrives
at
[eqs.
36-38]
for
N, T,
and O.
[Eq.
36]
and
[eq.
37]
can
be
read off from
[eq.
30]
on [p.
4] (see notes 18
and
13).
The
left-hand side of
[eq.
38]
is
found
by
using
[eq.
28]
on [p.
4]
and
replacing
T
by
Q.
The
right-hand
side is the
right-hand
side
of
[eq.
22]
on [p. 3]
with
the
sign
corrected
(see note
12).
The corrections from
1/r
to
r
in
[eq.
37]
and
[eq.
38]
are
in
Besso's hand
(see
[p.
4],
[eq.
28]
and
note
17); so
is the
addition of
the
factor
1/c20
to
the
right-hand
side
of
[eq.
38].
[Eq.
39]
gives
the
solution
to
[eqs.
36-38].
[26][Eq. 40]
and
[eq. 42] give
the
metric
field
for
a
static
sun to
second
order.
[Eq.
40]
is
obtained
by
inserting
the
solutions for
N, T,
and O in
[eq. 39]
into
[eq.
17] on
[p. 3]
and
adding
the
result
to
yuv
to first
order
in
[eq. 4] on [p.
1].
See
note 29
for
an
explanation
of how
one
quickly
arrives
at
the determinant of
this
metric
given
in
[eq. 41].