  We report measurements of the low temperature magnetic response of a line of
16 GaAs/GaAlAs \emph{connected} mesoscopic rings whose total length is much
larger than $l_{\phi}$. Using an on-chip micro-\textsc{squid} technology, we
have measured a periodic response, with period $h/e$, corresponding to
persistent currents in the rings of typical amplitude $0.40\pm 0.08 nA$ per
ring. Direct comparison with measurements on the same rings but \emph{isolated}
is presented.
