DOC.
7
GRAVITATIONAL INDUCTION
127
d_
dt
x_
c
N
dc
dx
1
-
\ 1
-q2
+
etc.
m
Here
x
=
dx/dt,
and
q
denotes the
velocity
of the material
point,
m
its
mass,
Rx
the force
acting
on it, c
the
velocity
of
light,
which
is to
be viewed
as a
function of
the
coordinates
x,
y,
z.
From these
equations
it
follows, among
other
things,
that
mc/1-q2/c2
is to be
regarded
as
the
energy
of the material
point,
and
m/2
q2/c,
in first
approximation,
as
its kinetic
energy.
In
order to obtain the kinetic
energy
in the
customary
unit,
one
has
to
multiply
this
expression by
the
constant
c0,
which
is
equal
to
the
velocity
of
light
at
infinity;
let the latter be
equal
to
the
average velocity
of
light
in
our gravitational potential.
Thus,
in the
customary
units the kinetic
energy
L
is
L
-
2
c
In order
to
know the
expression
for
L
for
an
arbitrary place,
we
still have
to
determine
c as a
function of
x y
z.
In accordance with the indicated
equation
of
motion,
for
a
sufficiently slowly
moving point subjected
to
no
forces aside from the
gravitational field,
dc
x
=
-c
-,
etc.,.
dx
or,
if
one
defines the
gravitational potential
O
in
a
similar
manner,
d0
dc
-
=
c
-,
etc..
dx dx
After
integration,
this
yields
with
sufficient
accuracy,
if
O0
denotes the
gravitational
potential
prevailing
at
infinity,
0
-
$
=
c0(c0
-
c)
=
Co
1
-
0
or
=
1
-
$0
-
*
Co
For the
material
point
in the interior
of
K,
$0
-
$
is
equal
to
kM/R,
so
that
one
obtains for
it
approximately
[5]
[6]