DOC. 14
EINSTEIN AND
BESSO MANUSCRIPT
391
[p.
15]
(Besso)
[72]On
[pp.
15-17],
a
summary
of
the
argument
on [pp.
1-14] is given.
This
summary
is
divided into
two parts.
In
the
first
part
the
general strategy
followed
on [pp.
1-7]
for
finding
the
metric
field
of the
sun
is
explained.
This
part
can
be found
on
[pp.
16-17].
The second
part,
on [p.
15], recapitulates
the calculations
on
[pp.
8-14]
for the
perihelion
motion
in
this
field.
Besso's discussion of
his
own
contributions
to
the calculations
([pp.
8-9]
and
[p.
14])
is
much
more
detailed than his discussion of Einstein's contributions.
[73][Eqs.
103-110]
are
in
essence
the main
steps
of the calculation
on
[p. 9].
There
are some
minor differences.
First,
the coefficient of
the A2/r2-term in
g44,
the
one
component
of
the
metric
field
in
[eq.
42]
on
[p.
6]
that
is
responsible
for the
perihelion
motion, is
left undetermined
(see
the
header of
[p.
15]
under
"2"
and
[eq. 106]).
Secondly,
the
A2/r2-term
in
[eq.
108]
is
taken
into
account
whereas
it
was
neglected
in
the corresponding
equation on [p. 9]
([eq.
66]).
This
does
not
make
any
difference,
however,
in
the
end
result. Other than
that,
almost
all
equations
on
[p.
15]
are equivalent
to
equations on [p. 9]:
[eqs.
103-104] to
[eqs.
58-59],
[eqs.
107-108] to
[eqs.
65-66],
and
[eqs.
109-110]
to
[eqs.
67-68].
On
the
left-hand side
of
[eq. 110],
the integral
sign
is
omitted.
[74]The rest
of
[p.
15]
summarizes the calculations
on [p.
14].
With
the
help
of
[eq.
84] on
[p.
11],
[eq.
110]
for the
angle
between
perihelion
and
aphelion
is
expressed
in terms
of the
roots
of the
polynomial
under the
square root sign
in
[eq.
110]
(see
the
first
step
in
[eq.
114]). Using
[eqs.
111-113]-equivalent to
[p.
14],
[eqs.
98-100] (see notes 68 and
69)-for
these
roots,
one
arrives
at
the
final
expression given
in
[eq. 114].
For
n
=
3/8,
the value of
n
for the metric
field
of
the
sun
in
[eq. 42] on
[p.
6]
(see
[eq. 106]
and
note 73), this
expression
is
seen to
be
equivalent
to
the
expressions
for the
angle
between
perihelion
and aphelion
given
in
[eq.
101]
on [p.
14]
(F
is
defined
in
[eq. 61]
on
[p. 9] as Bc20/E).