388
DOC. 42 SPECIAL AND GENERAL RELATIVITY
148
Relativity
ated
at
a
distance
y
from
the
centre
of the
disc,
has
a
velocity
relative
to
K which
is
given by
v
=
wy
where
w represents
the
angular
velocity
of rotation of the disc
K' with
respect to
K.
If
v0
represents
the
number
of
ticks of
the clock
per
unit
time
("rate"
of the
clock)
relative
to
K
when the clock
is
at
rest,
then the "rate"
of the clock
(v)
when
it
is
moving
relative
to
K
with
a
velocity v,
but
at rest
with
respect to
the
disc, will,
in accordance with Section
12,
be
given
by
v
=
v0/1
-
v2/c2,
or
with
sufficient
accuracy by
v
=
v0(1
1/2).
This
expression
may
also
be stated in
the
following
form:
v
=
v0(1
-
1/c2).
If
we
represent
the
difference of
potential
of
the
centrifugal
force
between the
position
of
the clock and the
centre
of
the
[94]
[95]