DOC.
23
151
The length
of the
rod,
measured
in
K,
is thus l/p(v); this establishes the
meaning
of
the function
p.
For
reasons
of
symmetry
it is obvious that the
length
of
a
rod
measured
in the
system
at
rest
and
moving
perpendicular
to
its
own
axis
can
depend only
on
its
velocity and not
on
the direction
and
sense
of
its motion.
Thus, the
length
of
the
moving
rod
measured in the
system
at
rest
does
not
change
when
v
is
replaced
by -v.
From
this
we
arrive
at
or
I
=
t
v(v)
(fi(-v)'
ip{v)
=
tp(-v).
It follows
from
this relation
and
the
one
found
before that
p(v) must
equal 1,
so
that the transformation
equations
obtained
become
ß t
J2 v
x
"
(
=
ß(x
-
vt),
y
= y
(=
z,
ß
l
-
V
[16]
where
§4. The
physical
meaning
of the
equations
obtained
concerning
moving
rigid
bodies
and
moving
clocks
We
consider
a
rigid
sphere1
of radius
R
that is
at
rest
relative
to [17]
the
moving system
k
and
whose
center
lies
at
the
origin
of
k.
The
equation
of the surface
of this
sphere, which
moves
with
velocity
v
relative
to
the
system
k,
is
1I.e.,
a
body possessing
the
shape
of
a
sphere
when
investigated at
rest.