254
DOC. 42 SPECIAL AND GENERAL RELATIVITY
8
Relativity
(b)
In
locating
the
position
of the
object,
we
make
use
of
a
number
(here
the
length
of the
pole
measured with the
measuring-rod)
instead
of
designated points
of reference.
(c)
We
speak
of the
height
of the cloud
even
when the
pole
which reaches
the cloud
has
not
been
erected.
By
means
of
optical
observations of the cloud
from
different
positions
on
the
ground,
and
taking
into
account
the
properties
of the
propagation
of
light,
we
determine the
length
of the
pole
we
should have
required
in
order
to
reach the cloud.
From
this
consideration
we
see
that it
will
be
advantageous
if,
in
the
description
of
position,
it should be
possible by
means
of numerical
measures
to
make ourselves
independent
of the existence of marked
positions (possessing
names)
on
the
rigid
body
of reference. In the
physics
of
measurement
this
is
attained
by
the
application
of the Cartesian
system
of
co-ordinates.
This
consists
of
three
plane
surfaces
perpendicular to
each
other and
rigidly
attached
to
a
rigid
body.
Referred
to
a
system
of
co-ordinates,
the
scene
of
any
event
will
be determined
(for
the main
part) by
the
specification
of the
lengths
of the three
[5]
perpendiculars
or
co-ordinates
(x,
y,
z)
which
can
be
dropped
from
the
scene
of the
event to
those three
plane
surfaces.
The
lengths
of these three
perpendiculars
can
be determined
by
a
series of
manipulations
with
rigid
measuring-rods performed
according
to
the rules and methods
laid
down
by
Euclidean
geometry.
In
practice,
the
rigid
surfaces which constitute the
system
of
co-ordinates
are
generally not
available; furthermore,
the
mag-
nitudes of the co-ordinates
are
not actually
determined
by