  Since the works of Haraux and Jaffard we know that rectangular plates may be
observed by subregions not satisfying the geometrical control condition. We
improve these results by observing only on an arbitrarily short segment inside
the domain. The estimates may be strengthened by observing on several
well-chosen segments.
  In the second part of the paper we establish various observability theorems
for rectangular membranes by applying Mehrenberger's recent generalization of
Ingham's theorem.
