  We present here the first experimental study of Wigner islands formed by
electrons floating over helium. Electrons are trapped electrostatically in a
mesoscopic structure covered with a helium film, behaving as a quantum dot. By
removing electrons one by one, we are able to find the addition spectrum, i.e.
the energy required to add (or extract) one electron from the trap with
occupation number $N$. Experimental addition spectra are compared with Monte
Carlo simulations for the actual trap geometry, confirming the ordered state of
electrons over helium in the island.
