DOC.
14 EINSTEIN AND
BESSO
MANUSCRIPT 403
[p.
21]
(Besso)
[100][Eq.
139] gives
expressions
for the
components
of
b
=
rot
g
for the metric
field in
[eq.
131]
on [p.
19]
(see
note 99).
[101]The
special case
of
an
orbit
in
the
plane
of rotation of
the
sun
is
considered. This
plane
is
chosen
to
be the
xyplane.
Hence,
ox
=
oy =
z
=
0.
For
this
special case,
[eq.
139]
reduces
to
[eq.
140],
and
[eq.
137]
on [p.
20]
reduces
to
[eq.
141] (the zcomponent
becomes
z
=
0).
In
the
equation
for
x
in
[eq.
141],
a
term

1/2dg44/dx
is
omitted
in
front of the second
equality
sign;
similarly, in
the
equation
for
y,
a
term
1/2dg44/dy
is
omitted
in
front of the second
equality
sign.
[102]In
[eqs.
141143],
an expression
for the
area velocity
f
=
1/2(xy

yx) is
derived
(see
the editorial
note,
"The EinsteinBesso
Manuscript on
the Motion of
the
Perihelion of
Mercury,"
sec.
II.2b, eq. (17)).
[103][Eqs.
144145]
give
the Hamiltonian for
a
unit
point mass moving
in the
xyplane,
the
plane
of rotation of
the
sun.
[Eq.
144] is
obtained
by inserting
[eq.
131] on
[p. 19]
for the metric
field
of the
sun
with
angular velocity
vector
o
=
(0, 0, o)
into
the
general expression
for the
Hamiltonian
in
the "Entwurf"
theory (see
[p.
8],
[eq.
50]). Inserting
[eq.
134] on
[p.
20]
for
ds/dt
into
[eq.
144],
one
obtains the
first line
of
[eq.
145].
This
expression
is
then
expanded to
first
order
in
the
quantities
A/r
and
q2/c20.