DOC.
47
261
V
=
ß
y
where
1
-
71
x
x]
-
ß{x
-
vt)
y
z
ß
=
1
1
(1)
vz
If
we
solve
equations
(1)
for
x, y, z,
and t,
we
obtain the
same
equations,
except
that the
"primed"
quantities
are
replaced
by
the
corre-
sponding "unprimed"
ones,
and
vice
versa,
and
that
v
is
replaced
by -v.
This also follows
directly
from
the principle
of relativity
and from
the fact
that, relative
to
S',
S
performs
a
parallel
translation with
velocity
-v
in the direction of the X'-axis.
In
general,
according to
the
principle of
relativity
each correct
rela-
tion
between
"primed"
(defined
with
respect
to
S')
and "unprimed"
(defined
with respect
to
S)
quantities
or
between
quantities
of
only
one
of these
kinds
yields
again
a
correct
relation if the
unprimed symbols are
replaced
by
the
corresponding
primed symbols,
or
vice
versa,
and
if
v
is
replaced
by
-v.
[22]
§4.
Inferences
from
the transformation equations
concerning
rigid bodies
and
clocks
1. Let
a
body
be at
rest
relative
to
S'.
Let
x1',
y1',
z1'
and
x2',
y2',
z2'
be
the
coordinates
of
two
material points
of
the
body
with
respect
to
S'. In accordance with the transformation
equations
just derived,
the
following
relations hold
between
the
x1, y1,
z1
and
x2, y2,
z2
coordinates
of
these points relative
to
the reference
system
S at
all
times t of
S: