DOC.
14
EINSTEIN AND
BESSO MANUSCRIPT
365
[p. 3]
(Einstein)
[10][Eq. 17] gives
the
form of
a
spherically symmetric
metric
in Cartesian coordinates
(see
[p.
7]
for
a
derivation). See note 29
for
an
explanation
of
how
one
quickly
arrives at
[eq.
19]
for the
determinant of
the
metric
in
[eq.
17].
[11]See
the editorial
note,
"The Einstein-Besso
Manuscript on
the Motion of
the
Perihelion of
Mercury,"
sec.
II.1a,
eq.
(2). Inserting
[eq.
4]
and
[eq.
5]
on [p.
1]
into
eq.
(2), one
arrives
at
[eq.
20],
[eq.
21], and
[eq.
22]
for
yxuv
(=
yuv).
The minus
sign
in
[eq.
22]
should
be
a
plus
sign.
(2)
[12]These
two
lines
are
in
Besso's hand. The
11-component
of
[eq. 17]
is
inserted for
yx11
in
[eq.
20].
The
two
lines
may
have
been added
in
connection
with
Besso's calculations
on [p. 51]
(see note 240).
[13][Eq.
23]
is
obtained
by
substituting
the
11-component
of
[eq. 17]
for
yx11
in
[eq.
20].
When
it
is
assumed
that the coefficients of
x2 on
the left-
and
right-hand
sides
of
[eq.
23]
are
equal
to
each
other,
[eq.
23]
breaks
up
into two
equations,
[eq.
24]
and
[eq.
25].
When the
12-component
of
[eq. 17]
is inserted
into
[eq.
21],
the latter
equation
turns into
[eq.
25],
hence Einstein's
remark that the
second
equation, i.e.
[eq.
21],
offers
nothing
new
("Zweite
Gleichung ergibt
nichts
Neues").
[Eq.
26]
is
obtained
by substituting
the
44-component
of
[eq. 17]
for
yx44
in
[eq.
22].
The
minus
sign
in
[eq. 26]
should
be
a
plus sign (see note
11).
[14]The
factor
3/8
should
be
5/8
(see
[eq.
40]
on [p.
6]).
The mistake
is
a
consequence
of the
mistake
in
[eq.
22]
(see note
11).