  By proper co-ordinates of non-inertial observers (shortly - proper
non-inertial co-ordinates) we understand the proper co-ordinates of an
arbitrarily moving local observer. After a brief review of the theory of proper
non-inertial co-ordinates, we apply these co-ordinates to discuss the
relativistic effects seen by observers at different positions on a rotating
ring. Although there is no relative motion among observers at different
positions, they belong to different proper non-inertial frames. The
relativistic length seen by an observer depends only on his instantaneous
velocity, not on his acceleration or rotation. For any observer the velocity of
light is isotropic and equal to $c$, provided that it is measured by
propagating a light beam in a small neighbourhood of the observer.
