DOC. 14
EINSTEIN
AND BESSO MANUSCRIPT
375
[p. 8]
(Besso)
[34]See the
editorial
note,
"The Einstein-Besso
Manuscript
on
the
Motion of
the
Perihelion of
Mercury,"
sec.
II.1b, for
a
brief outline of
the
calculations
on [pp.
8-15].
The
page
and
equation
numbers
given on [p.
8]
all
refer
to
Einstein and Grossmann
1913
(Doc. 13).
[35][Eq.
48]
is the
x-component
of
the
Euler-Lagrange equations
for
a
point
mass m
in
an
arbitrary
metric
field.
Jx
is
defined
as
dH/dx
and
&x as
dH/dx, where H
=
-m
ds/dt
is the
Lagrangian. Inserting eqs.
7
and
8
from Einstein and Grossmann
1913 (Doc.
13),
p.
7,
into
[eq.
48],
one
obtains
[eq. 49].
For
a
point
mass
moving slowly in
a
static
metric
field,
[eq.
49]
reduces
to
[eq. 54].
[36][Eq. 50]
is the
equation
for
the
Hamiltonian of
a mass
point
m
in
an
arbitrary
metric
field.
This
equation
is
copied
from
eq.
9
in
Einstein and Grossmann
1913
(Doc.
13), p.
7.
For
a
unit
point
mass
in
a
static metric
field,
[eq. 50]
reduces
to
[eq. 51].
The minus
sign
in
[eq. 51]
should
be
a
plus
sign.
This mistake
is
corrected
in
[eq. 55].
[37][Eq. 52]
for ds/dt
is copied
from
eq.
5
in
Einstein and Grossmann
1913
(Doc. 13), p.
7.
Inserting
[eq. 42]
for
the
metric
field
of
the
sun
into
[eq. 52]
and
neglecting terms
smaller
than
of order
A2/r2,
one
arrives
at
[eq.
53].
[38]As
a
consequence
of
[eq.
54]
one
has
[eq.
56],
which in the
manuscript
is
called
the
area
law ("Flächensatz";
for
a
discussion of
[eq.
56],
see
the
editorial
note,
"The Einstein-Besso
Manuscript
on
the
Motion of
the
Perihelion of
Mercury,"
sec.
II.1b).
In
[eq. 57]
the
so-called
"area
velocity"
f
("Flächengeschwindigkeit")
is
introduced. The
constant
B
multiplied
by c0
is
called
the
"area
law
constant"
("Flächensatzkonstante").