DOC. 14
EINSTEIN
AND BESSO
MANUSCRIPT
425
[p.
32]
(Einstein)
[140]The
Roman
numerals "II"
on [p.
32]
and
[pp.
34-35]
indicate that these
pages
deal with
the
perihelion
motion in the
field
of
a
rotating
rather than
a
static
sun
(see the
editorial
note,
"The Einstein-Besso
Manuscript on
the Motion of
the
Perihelion of
Mercury,"
footnote
25).
[141]The
calculations
on
the
top
half of
[p.
32]
in Einstein's hand
are
equivalent
to
the
cal-
culations
on [pp.
22-24] in
Besso's hand. Einstein
presumably
consulted Besso's calculations.
What
seems
to
be
a
clear indication of
this
is
the
use
of
the
quantity
S0 on [p.
32],
which
seems
to
derive from the
product
So
occurring
on
[pp.
22-24]
(compare,
for
instance,
S20
on
the second
line of
[eq.
191]
to S2o2
on
the last line of
[eq. 157] on [p. 23]).
But for the
use
of
S0
instead
of
So,
[eqs.
189-190]
are
the
same
as [eqs.
155-156]
on [p. 23]
(dt
in
[eq. 189]
should
be
dt2).
[Eq.
191]-for
the relation between
dr
and
dc
for
an
orbit
in
the
plane
of rotation of
the
sun-is
equivalent to
[p.
22],
[eq.
148];
[p.
23],
[eq.
157];
and
[p. 24], [eq. 166].
For further
discus-
sion,
see
the editorial
note,
"The Einstein-Besso
Manuscript on
the Motion of
the
Perihelion of
Mercury,"
sec.
II.2b.
[142]with
the
help
of
[eq.
84]
on [p.
11],
[eq. 191]
for
d(p
can
be
integrated
between
r1
and
r2
to find
the
angle
between
perihelion
and
aphelion. Inserting
a
=
S0/C
and
1/2(r'
+
r")
=
-
S0/C
(see
[eq.
193])
into
[eq.
84],
one
arrives
at
[eq. 192]
for the
integral.
[143][Eqs.
193-195]
give
the relation between
roots
and coefficients of
the polynomial
under
the
square
root
sign
on
the second line of
[eq.
191].
The derivation of
[eqs.
193-195]
is
completely
analogous to
the derivation of
[eqs.
98-100]
on [p. 14]
(or, equivalently,
[eqs.
111-113]
on
[p.
15])
for the
case
of
a
static
sun
(see notes 68
and
69).
[144]The
factor
C//2c0(c0
-
E) in
[eq. 196]
should
be
y/2c0(c0
-
E)/C. The calculation
is
continued
on [p.
34].