DOC. 14 EINSTEIN AND
BESSO MANUSCRIPT
399
[p. 19]
(Besso)
[88]After
[eq. 126]
(the x-component
of
[eq. 123] on [p.
18])
and
[eq.
127]
(=
[p. 18], [eq.
124])
are
inserted
into
[eq. 125]
(=
[p. 18], [eq. 121]),
the
integral giving
y14
is
evaluated
exploiting
the
spherical
symmetry
of
the
problem.
All
terms
with odd
powers
of
x, y, or
z
vanish.
Only
the
terms
with
f
d3x
p0 z2
=
f
d3x
p0
y2
=
1/3
/
d3x
p0
r2
survive. In
spherical
coordinates,
this
last
integral
becomes
4^/3
f
dr
p0
r4.
The end result for
yl4
is
given
in
[eq.
129]
(y44
is
the
same
as
for
a
static
sun; see
[eq.
130]).
[89]The comment
"factor
k
is
missing"
("Faktor
k
fehlt")
is
in
Einstein's hand. This
comment
may
have been added
in
connection
with
considerations
on [p.
34]
(see note
151).
[90]In
[eq.
128],
the
quantity
S is
defined
as
1/3
times the
moment
of inertia of
the
mass
distribution
representing
the
sun.
At
this
point,
the factor
k
is
not meant to be
part
of
S.
From
[eq. 138] on [p. 20]
onwards,
however,
it is
absorbed into
S.
[91]In the deleted
line
one recognizes
the
right-hand
side
of
[eq. 133] on [p.
20].
[92]There
are some
small
errors
in
[eqs.
131-132],
the
equations
for the metric field
of
a
rotating
sun
to first
order:
A/r
in
g44
should
be A/R at this
point (though
this
notation
is changed on
[p.
20],
see
note 98),
and
p0
in
y4i
should be Sk.