DOC.
14
EINSTEIN AND BESSO
MANUSCRIPT
393
[p.
16]
(Besso)
[75][P. 16]
is
the
verso
of
[p.
17],
a
letter from C.E.
Guye to
Einstein,
31 May
1913
(Vol.
5,
Doc.
443),
with calculations and
text
added
(see
note 82).
[Pp.
1617]
contain the section
on
the
approximation procedure
announced
on [p. 15]
(see
note 72
and the editorial
note,
"The
EinsteinBesso
Manuscript
on
the Motion of
the
Perihelion of
Mercury,"
sec.
II).
[76]Besso's question"Is
the
static
gravitational
field
[in
[eq.
4]]
a
special case or
is it
the
general case
reduced
to
special
coordinates?"
("Ist
...
geführtes")indicates
that Besso
clearly
understood that solutions
to
the "Entwurf"
field
equations
are
unique only
up
to
a
coordinate
transformation. The
question
Besso raises also
comes up,
now
in
the
context
of
the final
version
of the
general theory
of
relativity,
in
Einstein's
1915
perihelion paper
(Einstein 1915d,
p.
832).
Einstein writes that
he will
assume
that
his
solution
to
the
field
equations
is
unique up
to
a
coordinate transformation. The SchwarzschildDroste solution later vindicated this
assumption
(see
Earman and Janssen
1993,
pp.
140141,
pp.
157158).
[77]Calculations for the effect of solar
pressure
on
the metric
field
of
the
sun
can
be
found
on
[p. 51].
Besso's claim that solar
pressure
does
not
affect
the
results
reported
here
is
probably
based
on
the
fact that to second order,
the
pressure
terms in
the sun's
energymomentum
tensor
only
give
contributions
to
g11, g22,
and
g33,
and
not to
g44,
the
component responsible
for
the
perihelion
motion.
[78]At
this
point,
the discussion
moves
from zeroth
to
firstorder
approximation.
Note that
the "Entwurf"
field
equations are given
in
the form

Duv
= K(tßV
+
Tuv),
whereas
in
the
main derivation of the metric
field
of the
sun
([p.
1],
[pp.
36])
they were
used
in
the form
A^v =
Kc(0MV
+
#MV).
The motivation for this choice
may
have been that
only
g44
plays a
role
in
the
equation
of motion for
a
planet
in
the sun's
field, as
is
noted
explicitly
below.
[P.
16]
may
thus
be
related
to
[p.
2],
where
g44
is
computed using
Duv
=
K(t^v
+
T^v).
[79]The
restriction
to
cases
where differentiation does
not
change
the order of
magnitude
of
terms in
the
power
series
expansion
of
the
metric
field is too
narrow.
All
that
is
needed
to
make
the
approximation procedure
work is
that differentiation
changes
all terms
by
a
factor of
a
fixed
order of
magnitude (so
that,
for
instance,
secondorder derivatives of
a
secondorder
term
are
of
the
same
order of
magnitude
as
products
of
two
firstorder derivatives of firstorder
terms).
[80]The
numbers 7,
8,
and
9
here refer
to equation
numbers
in
Einstein and Grossmann
1913
(Doc.
13).
These
equation
numbers and the
corresponding equations can
also
be
found
on
[p.
8]
(see
[eqs.
4850]).
[81]The
condition
gm4
=
0
immediately
follows from the
assumption
that the metric
is
static.
So,
Besso's observation that the
vanishing
of Coriolis forces
in
the inertial
system
used for the
calculation does
not
entail
gu4 =
0 becomes
an
academic
point.