DOC.
3
STATICS OF GRAVITATIONAL FIELD
103
(6b)
x
m
-
c
dt\
N
m
dc
dx
1
-
«
N
+ flx
etc.
[19]
i
-1
However,
this
equation
is
only
admissible if the
energy principle
is
satisfied in the
form
Rq
=
E.
This
can
be demonstrated in the
following way.
If
one
writes
(6b)
in the form
d
f
x
dt
+
I|££
c OX
=
J®r
etc.,
multiplies
these
equations
successively by
x/c2 etc.,
and then
sums
them,
one
obtains
^ 1
2 -4
/
E+.
-E"d
c-
2
dt
+
E
C
)
C"
c
[20]
From this
we
obtain
the relation
we are
seeking
if
we
take into
account
that,
because
of
(8),
q2
_
1 m
and
d_
dt
[c
c_
+
m
E
c
E
[21]
Thus,
the
relationships
of the force
to
the laws of
momentum
and
energy
remain in
effect.
§3.
Remarks
on
the
Physical Meaning
of the
Static Gravitational Potential
If
we
measure
the
velocity
of
light
in
a
space
of
nearly
constant
gravitational
potential by
measuring
with
a
specific
clock the time needed
by
the
light
to
traverse
a
closed
path
of
a specified length,
then
we
always
obtain the
same
number for the
velocity
of
light totally independently
of the
magnitude
of the
gravitational potential
in the
space
in
which
we
carry
out
the measurement.6 This follows
directly
from
the
equivalence
principle.
Thus,
if
we
say
that the
velocity
of
light
at
a point
P
is
c/c0
6We
always use
the
same
clock for the time
measurements;
the clock
is
always brought
to the
place
for which
c
is
to
be
determined.