DOC.
14
EINSTEIN
AND
BESSO MANUSCRIPT
395
[p. 17]
(Besso)
[82][P.
17]
is
the
recto
of
a
letter from C.-E.
Guye to
Einstein,
31
May
1913
(Vol. 5,
Doc.
443). Only
the calculations
on
the
adjoining page
of
the
letter
are
transcribed. The
importance
of
this
page
for the
dating
of
the
manuscript
is
discussed
in the
editorial
note,
"The Einstein-Besso
Manuscript on
the Motion of the Perihelion of
Mercury,"
sec.
III.
[83]The two
equations to
the far
right,
for the covariant
energy-momentum
tensor
Tpv
and for
the determinant of
a
static,
spherically symmetric
metric
(see the
identical
[eq. 19] on [p.
3]),
are
the
only two equations
on
this
page
in
Einstein's hand. The matrix underneath these
two
equations
is
obtained
by
inserting power
series
expansions
in
1/r for the functions
N,
T,
and
R
into
[eq. 17] on [p. 3],
in
which these functions
were
introduced.
[84]The sentence
under
"b)" is
the
only sentence
Besso devotes
to explaining
the
strategy
for
finding higher-order
contributions
to
the metric
field
of the
sun.
[85]The
purpose
of the calculation
in
Newtonian mechanics that
takes
up
the
rest
of
[p. 17]
appears
to be to show
that the
quantities
q2/c20
and
A/r
are
of
the
same
order of
magnitude.
First,
Newton's second
law is
used
to
derive
energy
conservation
([eq.
115])
and
the
area
law
for
a
planet orbiting
the
sun.
[Eq.
116]
follows from the
area
law
(see
note
116;
va,p
and
da,p
are
the
planet's velocity
and
its
distance from the
sun
both taken
at
aphelion
and
perihelion,
respectively). Setting
the
energy at aphelion equal to
the
energy at perihelion (see
[eq.
117]),
one
can,
with the
help
of
[eq.
116], express
the ratio of
v2
and
2MK/r-or,
equivalently,
q2/c20
and
A/r-at
perihelion
and
aphelion
in terms
of
dp/da.
The
expression given
in
[eq.
118]
is
incorrect, however;
the left-hand
side
should
be
1
+
1-dp/da.
From
[eq.
118],
in
both
its
corrected
and
its
uncorrected
form, it
follows
that,
since
dp
and
da are
of
the
same
order of
magnitude, v2
and 2MK/r
are
of
the
same
order of
magnitude
as
well.
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