DOC.
3
STATICS OF GRAVITATIONAL
FIELD
105
will
read8
l1c1=l2c2.
Finally,
it should be mentioned that
equation
(5b)
also
agrees
with this
general
result. For it follows from this
equation,
and from the circumstance that the
gravitational
force
acting
on a mass m
is
equal
to
-m
grad c,
that the force
R
with
which
two
masses
situated in
a
potential
c
at
distance
r
from each other
attract
each
other is
given
in first
approximation by
&
=
ck
mm
4nr2
Thus,
this force
is
also
proportional
to
c.
Furthermore,
if
we
envision
a "gravitational
clock"
consisting
of
a mass m
that revolves around
a
fixed
mass
m'
at
a
constant
distance
R
under the sole influence of the
gravitational
force
of
m',
then,
according
to
(6b),
this
occurs
in
first
approximation according
to
the
equations
mx
=
c
etc.
From
this it follows that
m^R
=
c2k-^
47TR2
The
rate
go
of the
gravitational
clock is thus
proportional
to
c,
which should be the
case
for clocks of
any
kind.
§4.
General Remarks About
Space
and
Time
How
then,
does the above
theory
relate
to
the old
theory
of
relativity
(i.e., to
the
theory
of
the universal
c)?
In Abraham's
opinion,
the Lorentz transformation
equations
should hold in the
infinitesimally
small
just
as
before, i.e.,
there should be
an
x-t
transformation
such that
dx'
=
*
"
vdt
.
N
i-^
c2
[26]
8It is assumed
here,
though,
that
no
forces act
on
the massless thread stretched in the
gravitational
field. The
justification
for this will be
presented
in
a paper
that is
soon
to
follow.
[25]