DOC. 14 EINSTEIN AND BESSO MANUSCRIPT
431
[p.
35]
(Einstein)
[158]The equations at
the
head of
[p.
35]
are
all
essentially equivalent to equations
on
[p.
34]:
[eq. 208]
to
[eq.
202],
[eq. 209] (a
factor
n
is omitted
on
the right-hand
side) to
[eq.
203], and
[eq. 210]
to
[eq. 204].
Once
again,
the fact
that
the
expression
for
the
angle
between
perihelion
and
aphelion
is
dimensionless
(see note
151)
is
checked.
[159]The
three columns above
the
horizontal
line in the middle of
[p. 35] give
logarithms
of
the
various factors
in the
expression
for
the
retrogression
of
the perihelion
in [eq. 210].
Apparently,
it
was
only
after these calculations that
the
factor
162n/c02
in this
equation
was
changed to
162t/t2c20,
thus
correcting
the
error
in
[eq. 209].
For
the
numbers
in
the first column,
see [p.
34];
for
the
numbers
in the
second
and
third
columns,
see [p.
26].
K2 in the
second
column should
be
K-2
(see note
119).
Note
that 12.75946
=
log
a (see notes
122
and
157).
Subtracting log(K-2c20a6)
from log(2r
M
S0T3)
and
neglecting
the
eccentricity
e
of
Mercury's
orbit,
one
arrives
at
0.5120
-
8
for
the
logarithm
of
the
retrogression
of
Mercury's perihelion in
fractions of
c
per
half
a
revolution.
Due
to
the
error
in the
mass
of
the
sun
(see
note
120)
and the
omitted factor 1/n3
in
the
uncorrected version of
[eq. 210]
that
was
used, this
result
is
a
factor
100T3 too
large.
[160]The expression
2MS0T3/n2c20a6K-2
(see
[eq.
210]; at
this
point
the
corrected version of
this
equation
is
used)
is
evaluated
to
obtain
a
value for
the
retrogression
of
Mercury's perihelion
due
to the
rotation of
the
sun.
The
result, 8.7
•
10-10
[.t
radians
per
half
a
revolution],
is
a
factor
100
too large,
due
to the
error in
the
mass
of
the
sun
(see
note
120).
The various numbers
that
are
inserted
are
taken
from the
auxiliary
calculations
to
the
right (see notes 161-164),
with
the
exception
of
the values
10
and
1021
[cm2/s2]
inserted for
t2
and
c02,
respectively.
These crude
approximations
indicate
that, at
least
at
this
point,
Einstein
was
concerned
only
with
the
order
of
magnitude
of
the
effect of
the
sun's rotation
on
Mercury's perihelion.
[161]In
[eq.
211], the
mass
M
of
the
sun
is computed
via the
relation
M
=
(M
/ Me)pe
Ve
(see
note 120).
The corrections
are
in
Besso's hand.
[162][Eq.
212]
(=
[eq.
207]
on [p.
34])
is used to
compute
S0.
The radius
R
of
the
sun
is
computed
via the
relation
R
=
(R/Re)Re (see
note
155).
Note
that
R2
=
4.8
•
1021
cm2.
The
correction
in
[eq. 212]
is
in
Besso's
hand.
[163]The period
T
of
Mercury's
orbit around
the
sun
is
converted
from
days to
seconds
(see
note
121).
[164]In
[eq.
213],
the
semi-major
axis
a
of
Mercury's
orbit
is computed
via the
relation
a
=
(rm/re)re (see note
122).
[165][Eq.
214]
is in
Besso's hand.
It
is
a
calculation of
the
gravitational
constant K via the
relation
K
=
r3co2/M.
The
same
relation
is
used
on
[p.
30]
(see note
134)
and
on
[p.
42]
(see
note
196).
The value for
T,
the
period
of
the Earth's revolution around
the
sun,
that
is
inserted
into
co
=
2tc/T, is
a
factor
10 too
small.
The
value
inserted for
M,
the
mass
of
the
sun,
is
a
factor
10 too
large.
As
a
consequence,
the end
result for
K
is
a
factor
10 too
large.