  We show that in a ring-shaped Luttinger Liquid (LL) in contact with an
electron reservoir --- the chemical potential in the ring being controlled by a
gate voltage $V_g$ --- both the average ring charge and the persistent current
in the ring are step-like functions of $V_g$ at low temperatures. The step
positions are determined by the LL parameter $\alpha=v_F/s$, which therefore
can be directly measured. We study electrons both with and without spin, taking
into account long-range interactions in the ring.
