DOC. 4 THEORY OF STATIC GRAVITATIONAL FIELD
117
power
of
c (cB).
In the
case
where
q
#
0,
the force would also
depend
on q;
this
dependence
must
be such that the
gravitational
mass
of
a
box that contains
moving
elastic material
points depends
on
the
velocity
of motion
of
the
points
in the
same
way
as
the
gravitational
mass.
In view
of
the results of the old
theory
of
relativity,
this
can
only
be achieved
by
the
postulate
e
,
-m
grad
c
.
const.
N
l-q2
c2
If
one
substitutes
Rxs
in the
equations
of motion
accordingly,
then
one can
prove
that
Rxax +
Ryay
+
RZaZ
can
represent
a
time derivative
only
in the
case
where the
constants
a
and
ß
are
given
values that result in the
equations
of
motion
presented
in the
previous paper.
One will therefore have
to
stick with them and
to
the
[25]
expression
(4)
for the force that results from them
if
one
does
not want to
give up
the
whole
theory (determination
of the static
gravitational
field
by c).
Thus,
it
seems
that the
only way
to avoid
a
contradiction with
the
reaction
principle
is
to
replace equations
(3)
and
(3a)
with other
equations homogeneous
in
c
for which the reaction
principle
is
satisfied when the force
postulate
(4)
is
applied.
I
hesitate
to
take this
step
because
by doing
so
I
am
leaving
the
territory
of
the
unconditional
equivalence principle.
It
seems
that the latter
can
be maintained for
inifinitely
small fields
only.
Our derivations of the
equations
of
motion
of
the
[26]
material
point
and of
the
electromagnetic equations
do
not
thereby
become
illusory,
because
they apply equations
(2) only
to
infinitesimally
small
spaces.
For
example,
these
derivations
can
also be tied
to
the
more
general equations
dc
=x+
c~
2
(=z,
Ct,
where
c
is
an
arbitrary
function
of
x.-
If
one
reformulates the
integral
Ac
J
-
grad
cdr
c
(which
is
extended
over an arbitrary
volume)
in
a
suitable
manner,
one can easily see
for oneself that the reaction
principle
is satisfied if
one
retains
(4)
while
replacing
equation
(3a)
with the
equation