DOC.
405
DECEMBER
1917 415
is obtained,
or
approximately
enough
9#44
•
,
%44
.
,
\
,
d2xA
X
+
-7T-y+-
+
dx
dy
u )
dsI
2
It
is
this
expression
which indicates
the
vanishing
of
the
last
equation
of motion.[5]
For
dx4/ds,
one
obtains,
if
one
sets for
the
guv's
(incorrectly,
by
the
way)
-1
0 0 0
0
-1
0 0
0 0
-1
0
0 0 0
g44
dx4
1
ds
=
1
V2
The
root of
your
error
lies
in
that
1/1-v2
cannot be inserted in its
place,[6] since
d/dt(g44)
and
d/dt(v2)
are
of
the
same
order of
magnitude.-
I probably
do
not
understand
your
first
difficulty.[7]
You
say entirely correctly:
If
I
were
within
the interior of
a
rotating, hollow
rotational
body, mechanically
I
would have
to
find
myself
to be in
the
state of
a
rotational
system
when
I
am
“at rest.”
A point of
mass
must
be able
to
move
in
a
circle
free of forces
when
it
is
moving
at
a
suitable
angular velocity
around
the
Z-axis
(in
the rotational
body’s
sense
of
motion).
Now, you
require, however,
that
d2x/ds2
vanish
for
such
a
point
when it
is
on
the
X-Z
plane.
This does
not
apply
to
rotational
motion,
though.
What
must
rather
apply
is
cPx
ds2
=
-w'2r
=
-w'2x,
whereby
w' is
the
point’s
rot.
velocity,
which
ought
to relate to
your
w
as
w'2
=
Cw2.
Your
equation
then
yields, as
it
should,[8]
2C
=
-C'.
The
fact that this
cannot be otherwise
is, incidentally,
guaranteed
by
the
general
covariance of all
equation systems
in
the
theory.-[9]