DOC. 42 SPECIAL AND GENERAL
RELATIVITY 277
TEN
On the
Relativity
of
the
Conception
of
Distance
Let
us
consider
two
particular points
on
the
train1
trav-
elling along
the embankment
with the
velocity
v,
and
inquire as
to
their
distance
apart.
We
already
know
that
it
is
necessary to
have
a
body
of reference
for
the
mea-
surement
of
a
distance,
with
respect to
which
body
the dis-
tance
can
be measured
up.
It
is
the
simplest plan to
use
the
train itself
as
reference-body
(co-ordinate
system).
An
ob-
server
in
the
train
measures
the interval
by marking
off
his
measuring-rod
in
a straight
line
(e.g.
along
the
floor
of the
carriage)
as
many
times
as
is necessary to
take him from the
one
marked
point to
the other.
Then
the number which tells
us
how often the rod
has
to
be
laid
down
is
the
required
distance.
It
is
a
different
matter
when
the
distance
has
to
be
judged
from
the
railway
line. Here the
following
method
suggests
itself.
If
we
call
A' and
B’
the
two
points
on
the train whose
distance
apart
is
required,
then
both
of
these
points
are mov-
1
E.g.
the middle of the
first
and of the
twentieth
carriage.
32