352
EINSTEINBESSO
ON THE MERCURY
PERIHELION
Some numerical calculations for the effect
are
found
on [p.
26],
[pp.
2830]
and
[p.
40]
of
the
manuscript.
On
[p.
28],
[p.
29], and
[p.
40]
the
number 3.4
•
106
is
given
for
the advance of
Mercury's perihelion
in
fractions of
n
per
half
a
revolution. Converted
to
seconds of
arc
per century,
this works
out to
1821",
the end
result
given on [p. 28].[38]
The number 3.4
•
106, however,
is
a
factor
100 too
large.
There
is
a
mistake of
a
factor
10
in
the
mass
of the
sun,[39] a
quantity
that
occurs
squared
in
the
expression
used
to
evaluate the
perihelion
advance
per
half
a
revolution.
On
[p.
30],
the mistake
in
the
mass
of
the
sun
is
corrected. A
new
calculation
with several other
errors
leads
to
a perihelion
advance of
1.65
•
108
in
fractions of
n
per
half
a
revolution.[40]
Immediately
below
this result,
the number 3.4
•
108
is
given.[41]
This would
give
the
correct
value of
18"
per century,
but this
new
number
is
not
converted
to
seconds of
arc per
century,
neither
on [p.
30] nor anywhere
else
in
the
manuscript.
2a.
Field
of
a
rotating sun
to
first
order
([pp.
1819]).
For
a
slowly,
uniformly,
and
rigidly rotating spherically symmetric mass
distribution
representing
the
sun,
the
leading
terms
in the
energymomentum
tensor
are ([p. 18], [eq. 119])
©4i
=
©i4
= (PO/Cq)
Xt, ©44
=
Po/Co
(11)
The other
components can
be
neglected. Accordingly,
the
4/xcomponents are
the
only
nontrivial
components
of the "Entwurf"
field
equations
in first
approximation (see
[p.
18],
[eq.
120]).
The
44component
is
the
same as
for the
case
of
a
static
sun.
In
modern
notation,
involving
the Dirac delta
function,
the
4/components
become
A
yl(k)
=
^r f
d3x8(X
x)p0(r)xi,
(12)
c0
J
where X
are
the coordinates of
an
arbitrary point at
large
distance from the
sun,
x
the
coordinates
of
points
in
the interior of
the
sun,
and
r
=
\x .
The
origin
of
the
coordinate
system
to
which both
X
and
x
refer
is
chosen
to be at
the
center
of
the
sun.
The solution
of
eq.
(12) is
given by
(see
[p.
18],
[eq.
121])
(1 ^
K
f
^
Poir)ki
Y4i
{X)
=

/
d5x
,
(13)
c2
J
An R'
*
\
where R'
=
\X

x\.
The
velocity
x can
be
written
as
the vector
product
of
the
angular
velocity
vector ("Drehungsvektor")
o
and
x ([p. 18], [eq.
123]).[42]
Expanding
1/R' in
[38]See
also
[p.
29],
where the end result
is
given
as
1.84
•
103.
[39]See
[p.
26], note 120.
[40]See
[p.
30],
[eq.
188]
and
note 135.
[41]See
[p.
30],
note 136.
[42]In the
manuscript,
a
Gothic
q
and
a
Gothic
r are
used
to
represent
x
and
x, respectively.
The
vector
product
of
two arbitrary
vectors is
written
as
"[.,.]."