262
THE
RELATIVITY PRINCIPLE
x2
-
xt
= 1
-
IJ2
~
Ui
~
V2
*2
-
*1
= ^2
/
1
•^r (®2
2/1
«1
I
-
V)
(2)
The
kinematic
shape
of
a body
undergoing
uniform translational
motion
thus
always depends
on
its
velocity relative
to
the
reference
system;
actually, the
body's
kinematic
shape
differs from its
geometric shape
only by
a
contraction in the direction
of
the relative
motion
in the ratio
of
1:
1
-v2/c2.
A
relative
motion of
reference
systems
with
superlightvelocity
is
not compatible
with
our
principles.
2. In the coordinate origin
of S'
let there
be
set
up
a
clock
at rest
which
runs v0
times faster than the clocks
used
for
measuring
the time
in
S
and
S',
i.e., this clock shall
complete
v0
periods
during
the time
a
clock
at rest
relative to
it,
of
the
type
used
for
measuring
time in
S and
S',
increases its
reading
by
one
unit.
How
fast
does
the first
clock
run as
observed
from
system
S?
The
clock considered
completes
one
period
in the time
epochs
t'n
=
n
where
n runs
through
the
integers, and
x'
=
0
for the
clock
at
all
times.v0,
Using
the first
two
transformation
equations,
one
obtains for the time
epochs
tn
in
which
the clock,
as
viewed from S,
completes
one
period:
t
=
ßV
=
n h n
v0
n
Thus,
observed
from
the
system
S,
the
clock
completes
v
2
1
nr
CZ
periods
per
unit
time;
or:
the
rate
of
a
clock
moving
uniformly
with
velocity
v
relative
to
a
reference
system
is slower
in the ratio
1
:
'1
1
-
v
u
as
observed
from
this
system,
than that of the
same
clock
when at rest
relative
to
that
system.