DOC. 42 SPECIAL AND GENERAL RELATIVITY 285
TWELVE
The
Behaviour
of
Measuring-Rods
and
Clocks
in Motion
I
place a
metre-rod in the
x'-axis
of
K'
in
such
a manner
that
one
end
(the
beginning)
coincides with the
point
x'
=
0,
whilst
the
other
end (the
end of
the
rod)
coincides with
the
point
x'
=
1.
What
is
the
length
of the metre-rod
relatively
to
the
system K?
In order
to
learn
this,
we
need
only
ask where
the
beginning
of the
rod
and the end of the
rod
lie
with
respect to
K
at
a
particular
time
t
of the
system K.
By means
of the first
equation
of
the Lorentz transformation the values
of these
two points at
the time
t
=
0
can
be shown
to
be
[17]
x
=
0
(beginning
of
rod)
x(end of
rod)
1-v2/c2
the distance between
the
points
being
1-v2/c2.
But the
metre-
40