108
DOC.
4
THEORY OF STATIC GRAVITATIONAL FIELD
primed
in order
to
indicate that
they pertain
to
the
system
E.
These
equations
are
to
be transformed
to
the
uniformly
accelerated
system
K in accordance with
equations
that,
for
sufficiently
small
t,
and
given an
appropriate
choice
of
coordinate
axes
and
initial
times,
may
be written in the form: [6]
(2)
5
=
x
+
ac
2
2
n
=
y,
C
=
z,
T
=
ct,
where
c
= c0
+
ax.
We also
want to
transform the field
vectors @'
and
@'
to
the accelerated
system
K.
We do this
by stipulating
that the field
vectors @
and
@,
which refer
to
K,
should
be identical with the field
vectors
@'
and
S'
of that unaccelerated
system
E with
respect
to
which the
system
K has
precisely
the
velocity
zero.
For
t
=
T
=
0 this
stipulation yields directly
@
=
@',
We make
an
analogous stipulation regarding
the electric
density, so
that for
t
=
T
=
0
P =
P'.
Now
we
note
that
it
suffices
if
the
transformed
equations
that
correspond
to equations
(1) are
set
up
for
t
=
t
=
0,
since these
equations
must, indeed,
be the
same
for
every
t.
For
t
=
x

0
we
have
according
to
(2)
A
=
A
A
=
A
A
=
A
d£
dx'
drj
dy'
d(
dz
It
already
follows from
what has been said
up
to
now
that the omission
of
the
prime
marks leaves the
righthand
sides of
(1) unchanged,
and likewise the lefthand sides
of the second and fourth of
equations
of
(1). Only
the transformation
of
the left side
of the
first and third of
equations
(1)
requires
some
reflection.
First of
all,
it
follows from
(2)
that for
a moving point
at
time
t
=
0
dx
=
d£,
dy =dn,
dz
=
dC,
(2a)
dt
=dr,
c